ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

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Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.

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Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

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Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic () and stochastic () basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., ), epidemic can still grow initially (if ) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.

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Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We consider a stochastic partial differential equation (SPDE) driven by a Lévy white noise, with Lipschitz multiplicative term . We prove that, under some conditions, this equation has a unique random field solution. These conditions are verified by the stochastic heat and wave equations. We introduce the basic elements of Malliavin calculus with respect to the compensated Poisson random measure associated with the Lévy white noise. If is affine, we prove that the solution is Malliavin differentiable and its Malliavin derivative satisfies a stochastic integral equation.

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Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

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Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic () and stochastic () basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., ), epidemic can still grow initially (if ) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.

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Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We consider a stochastic partial differential equation (SPDE) driven by a Lévy white noise, with Lipschitz multiplicative term . We prove that, under some conditions, this equation has a unique random field solution. These conditions are verified by the stochastic heat and wave equations. We introduce the basic elements of Malliavin calculus with respect to the compensated Poisson random measure associated with the Lévy white noise. If is affine, we prove that the solution is Malliavin differentiable and its Malliavin derivative satisfies a stochastic integral equation.

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Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations (2017)

Hindawi

In: International Journal of Stochastic Analysis

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Publication Date: 2017

Description: We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.

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Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations (2017)

Jin, Sixian ; Schellhorn, Henry

Hindawi

In: International Journal of Stochastic Analysis. 2017; 2017: 1-12. Published 2017 Feb 27. doi: 10.1155/2017/2876961.

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Publication Date: 2017-02-27

Description: We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.

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Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease (2017)

Otunuga, Olusegun Michael

Hindawi

In: International Journal of Stochastic Analysis. 2017; 2017: 1-7. Published 2017 Jan 23. doi: 10.1155/2017/6313620.

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Publication Date: 2017-01-23

Description: We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R0) and stochastic (R0) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R01) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.

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On (h0,h)-stability of autonomous systems (1992)

Liu, Xinzhi

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 331-337. Published 1992 Jan 01. doi: 10.1155/s1048953392000285.

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Publication Date: 1992-01-01

Description: In this paper, we discuss the qualitative behavior of a map h along solutions of an autonomous system whose initial values are measured by a second map h0. By doing this, we may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Five theorems on asymptotic stability are given and two examples are worked out.

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Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise (2017)

Balan, Raluca M. ; Ndongo, Cheikh B.

Hindawi

In: International Journal of Stochastic Analysis. 2017; 2017: 1-9. Published 2017 Mar 12. doi: 10.1155/2017/9693153.

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Publication Date: 2017-03-12

Description: We consider a stochastic partial differential equation (SPDE) driven by a Lévy white noise, with Lipschitz multiplicative term σ. We prove that, under some conditions, this equation has a unique random field solution. These conditions are verified by the stochastic heat and wave equations. We introduce the basic elements of Malliavin calculus with respect to the compensated Poisson random measure associated with the Lévy white noise. If σ is affine, we prove that the solution is Malliavin differentiable and its Malliavin derivative satisfies a stochastic integral equation.

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Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications (2017)

Merino, Raúl ; Vives, Josep

Hindawi

In: International Journal of Stochastic Analysis. 2017; 2017: 1-16. Published 2017 Jul 31. doi: 10.1155/2017/8019498.

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Publication Date: 2017-07-31

Description: We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

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On a multilevel controlled bulk queueing system MX/Gr,R/1 (1992)

Abolnikov, Lev ; Dshalalow, Jewgeni H.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 237-260. Published 1992 Jan 01. doi: 10.1155/s1048953392000200.

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Publication Date: 1992-01-01

Description: The authors introduce and study a class of bulk queueing systems with a compound Poisson input modulated by a semi-Markov process, multilevel control service time and a queue length dependent service delay discipline. According to this discipline, the server immediately starts the next service act if the queue length is not less than r; in this case all available units, or R (capacity of the server) of them, whichever is less, are taken for service. Otherwise, the server delays the service act until the number of units in the queue reaches or exceeds level r.The authors establish a necessary and sufficient criterion for the ergodicity of the embedded queueing process in terms of generating functions of the entries of the corresponding transition probability matrix and of the roots of a certain associated functions in the unit disc of the complex plane. The stationary distribution of this process is found by means of the results of a preliminary analysis of some auxiliary random processes which arise in the first passage problem of the queueing process over level r. The stationary distribution of the queueing process with continuous time parameter is obtained by using semi-regenerative techniques. The results enable the authors to introduce and analyze some functionals of the input and output processes via ergodic theorems. A number of different examples (including an optimization problem) illustrate the general methods developed in the article.

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Existence of solution to transpiration control problem (1992)

Zhu, Guanstian ; Wu, Jingang ; Liang, Benzhong ; [et al.]

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 339-361. Published 1992 Jan 01. doi: 10.1155/s1048953392000297.

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Publication Date: 1992-01-01

Description: Transpiration control can avoid change of the shape of a high-speed vehicle resulting from ablation of the nose, therefore also can avoid the change of the performance of Aerodynamics. Hence it is of practical importance. A set of mathematical equations and their boundary conditions are founded and justified by an example of non-ablation calculation in reference [1]. In [2], the ablation model is studied by the method of finite differences, the applicable margin of the equations is estimated through numerical calculation, and the dynamic responses of control parameters are analyzed numerically. In this paper we prove that the solution to transpiration control problem given in [1] exists uniquely under the assumption that the given conditions (i.e. given functions) are continuous.

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A note on the convexity of the expected queue length of the M/M/s queue with respect to the arrival rate: a third proof (1992)

Mehrez, A. ; Brimberg, J.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 325-329. Published 1992 Jan 01. doi: 10.1155/s1048953392000273.

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Publication Date: 1992-01-01

Description: The convexity of the expected number in an M/M/s queue with respect to the arrival rate (or traffic intensity) is well known. Grassmann [1] proves this result directly by making use of a bound on the probability that all servers are busy. Independently, Lee and Cohen [2] derive this result by showing that the Erlang delay formula is a convex function. In this note, we provide a third method of proof, which exploits the relationship between the Erlang delay formula and the Poisson probability distribution. Several interesting intermediate results are also obtained.

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Note on the inequalities of J. Kazdan (1992)

Lee, Will Y.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 375-379. Published 1992 Jan 01. doi: 10.1155/s1048953392000315.

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Publication Date: 1992-01-01

Description: In this note, we prove the Kazdan's inequalities without using what is called the Heisenberg uncertainty principle. Instead we prove it using Garofalo-Lin inequality among other things.

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Existence of approximate solution to abstract nonlocal Cauchy problem (1992)

Byszewski, L.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 363-373. Published 1992 Jan 01. doi: 10.1155/s1048953392000303.

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Publication Date: 1992-01-01

Description: The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

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Asymptotic classification of aliasing structures (1992)

Izmailov, R. N. ; Pokrovskii, A. V.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 193-203. Published 1992 Jan 01. doi: 10.1155/s1048953392000169.

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Publication Date: 1992-01-01

Description: The effects of quantization of quickly oscillating functions are considered. An asymptotical classification of aliasing spots is considered. The results obtained may be used in the restoring of certain features of initial functions.

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On a first passage problem in general queueing systems with multiple vacations (1992)

Dshalalow, Jewgeni H.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 177-192. Published 1992 Jan 01. doi: 10.1155/s1048953392000157.

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Publication Date: 1992-01-01

Description: The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing process explicitly. Various examples and applications are discussed.

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A generalized upper and lower solutions method for nonlinear second order ordinary differential equations (1992)

Nieto, Juan J. ; Cabada, Alberto

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 157-165. Published 1992 Jan 01. doi: 10.1155/s1048953392000133.

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Publication Date: 1992-01-01

Description: The purpose of this paper is to study a nonlinear boundary value problem of second order when the nonlinearity is a Carathéodory function. It is shown that a generalized upper and lower solutions method is valid, and the monotone iterative technique for finding the minimal and maximal solutions is developed.

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Generalized two point boundary value problems. existence and uniqueness (1992)

Murty, K. N. ; Sivasundaram, S.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 147-156. Published 1992 Jan 01. doi: 10.1155/s1048953392000121.

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Publication Date: 1992-01-01

Description: An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

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Controllability of nonlinear Volterra integrodifferential systems with prescribed controls (1992)

Balachandran, K. ; Lalitha, D.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 139-146. Published 1992 Jan 01. doi: 10.1155/s104895339200011x.

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Publication Date: 1992-01-01

Description: Sufficient conditions for the global controllability of nonlinear Volterra integrodifferential systems with prescribed controls are derived. The method is a transformation of the given control system into a boundary value problem and then the result is obtained by the application of the Schaefer fixed point theorem.

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On the unsteady flow of two visco-elastic fluids between two inclined porous plates (1992)

Sengupta, P. R. ; Ray, T. K. ; Debnath, L.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 131-138. Published 1992 Jan 01. doi: 10.1155/s1048953392000108.

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Publication Date: 1992-01-01

Description: This study is concerned with both hydrodynamic and hydromagnetic unsteady slow flows of two immiscible visco-elastic fluids of Rivlin-Ericksen type between two porous parallel nonconducting plates inclined at a certain angle to the horizontal. The exact solutions for the velocity fields, skin frictions, and the interface velocity distributions are found for both fluid models. Numerical results are presented in graphs. A comparison is made between the hydrodynamic and hydromagnetic velocity profiles. It is shown that the velocity is diminished due to the presence of a transverse magnetic field.

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Integral manifolds of impulsive differential equations (1992)

Bainov, D. D. ; Kostadinov, S. I. ; Van Minh, N. ; [et al.]

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 99-109. Published 1992 Jan 01. doi: 10.1155/s1048953392000078.

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Publication Date: 1992-01-01

Description: The present paper is concerned with the existence of integral manifolds of impulsive differential equations as t→+∞. Under the assumption of exponential trichotomy on the linear part of the right-hand side of the equation, it is proved that if the nonlinear perturbation is small enough, then there exist integral manifolds as t→+∞ for the perturbed equations.

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Impulsive integral equations in Banach spaces and applications (1992)

Guo, Dajun

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 111-122. Published 1992 Jan 01. doi: 10.1155/s104895339200008x.

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Publication Date: 1992-01-01

Description: In this paper, we first use the fixed point theory to prove two existence theorems of positive solutions for the impulsive Fredholm integral Equations in Banach spaces. And then, we offer some applications to the two-point boundary value problems for the second order impulsive differential equations in Banach spaces.

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Numerical solutions of nonstandard first order initial value problems (1992)

Venkatesulu, M. ; Srinivasu, P. D. N.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 69-82. Published 1992 Jan 01. doi: 10.1155/s1048953392000054.

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Publication Date: 1992-01-01

Description: Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P) y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.

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Problem of uniqueness in the renewal process generated by the uniform distribution (1992)

Ugrin-parac, D.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 291-305. Published 1992 Jan 01. doi: 10.1155/s1048953392000248.

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Publication Date: 1992-01-01

Description: The renewal process generated by the uniform distribution, when interpreted as a transformation of the uniform distribution into a discrete distribution, gives rise to the question of uniqueness of the inverse image. The paper deals with a particular problem from the described domain, that arose in the construction of a complex stochastic test intended to evaluate pseudo-random number generators. The connection of the treated problem with the question of a unique integral representation of Gamma-function is also mentioned.

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Boundedness and asymptotic stability in the large of solutions of an ordinary differential system y' = f(t, y, y') (1992)

Venkatesulu, M. ; Srinivasu, P. D. N.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 261-274. Published 1992 Jan 01. doi: 10.1155/s1048953392000212.

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Publication Date: 1992-01-01

Description: Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and solutions have been known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier existence of solutions of first order initial value problems and stability of solutions of first order ordinary differential system of the above type were established. In this paper we study boundedness and asymptotic stability in the large of solutions of an ordinary differential system of the above type under certain natural hypotheses on f.

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Existence of solutions of functional differential inclusions (1992)

Anguraj, A. ; Balachandran, K.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 315-323. Published 1992 Jan 01. doi: 10.1155/s1048953392000261.

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Publication Date: 1992-01-01

Description: We prove the existence of solutions of a functional differential inclusion. By using the variation of parameters formula we convert the functional differential inclusion into an integral inclusion and prove the existence of a fixed point of the set-valued mapping with the help of the Kakutani-Bohnenblust-Karlin fixed point theorem.

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Number of real roots of a random trigonometric polynomial (1992)

Farahmand, K.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(4): 307-313. Published 1992 Jan 01. doi: 10.1155/s104895339200025x.

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Description: We study the expected number of real roots of the random equation g1cosθ+g2cos2θ+…+gncosnθ=K where the coefficients gj's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, (j=1,2,…,n), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

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Convergence rates for empirical Bayes two-action problems: the uniform U(0,θ) distribution (1992)

Tahir, Mohamed

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 167-175. Published 1992 Jan 01. doi: 10.1155/s1048953392000145.

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Publication Date: 1992-01-01

Description: The purpose of this paper is to study the convergence rates of a sequence of empirical Bayes decision rules for the two-action problems in which the observations are uniformly distributed over the interval (0,θ), where θ is a value of a random variable having an unknown prior distribution. It is shown that the proposed empirical Bayes decision rules are asymptotically optimal and that the order of associated convergence rates is O(n−α), for some constant α, 0

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33

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Multipoint focal boundary value problems on infinite intervals (1992)

Umamaheswaram, S. ; Rama, M. Venkata

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 283-289. Published 1992 Jan 01. doi: 10.1155/s1048953392000236.

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Description: For the differential equation y(n)=f(x,y), we state a set of necessary and sufficient conditions for the existence of a solution (i) on a semi-infinite interval for a k-point right focal boundary value problem and (ii) on (−∞,∞) for a (n−1)-point right focal boundary value problem. The conditions are in terms of the existence of a pair of solutions u(x), v(x) satisfying some auxiliary boundary conditions and algebraic inequatilities.

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Lyapunov stability theory for dynamic systems on time scales (1992)

Kaymakçalan, Billur

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 275-281. Published 1992 Jan 01. doi: 10.1155/s1048953392000224.

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Description: By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

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A first passage problem and its applications to the analysis of a class of stochastic models (1992)

Abolnikov, Lev ; Dshalalow, Jewgeni H.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 83-97. Published 1992 Jan 01. doi: 10.1155/s1048953392000066.

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Description: A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models).Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated by a number of numerical examples and then are applied to a bulk queueing system with a service delay discipline.

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Extremal solutions to a class of multivalued integral equations in Banach space (1992)

Aizicovici, Sergiu ; Papageorgiou, Nikolaos S.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 205-220. Published 1992 Jan 01. doi: 10.1155/s1048953392000170.

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Publication Date: 1992-01-01

Description: We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a bang-bang theorem for a class of nonlinear, infinite dimensional control systems.

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Existence of a solution of a Fourier nonlocal quasilinear parabolic problem (1992)

Byszewski, Ludwik

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 43-67. Published 1992 Jan 01. doi: 10.1155/s1048953392000042.

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Description: The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder's theorem is used. The paper is a continuation of papers [1]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

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Admissible relaxation in optimal control problems for infinite dimensional uncertain systems (1992)

Ahmed, N. U. ; Xiang, X.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 227-236. Published 1992 Jan 01. doi: 10.1155/s1048953392000194.

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Publication Date: 1992-01-01

Description: In this paper we present a result on admissible relaxation for a class of systems governed by an uncertain evolution equation on Banach space. We show that the set of original trajectories is dense in the set of relaxed trajectories and that under certain assumptions the relaxed system is equivalent to the original system.

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39

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Existence of solution for a mixed neutral system (1992)

Balachandran, K. ; Anguraj, A.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(3): 221-226. Published 1992 Jan 01. doi: 10.1155/s1048953392000182.

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Publication Date: 1992-01-01

Description: We prove the existence of unique solution of the mixed neutral system x′(t)=f(t,x)+∑j=1mAj(t,x)x′(t+pj)+g(t,x,x′(t+h))x(0)=x0 and also prove the continuous dependence of the solution.

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General algorithm and sensitivity analysis for variational inequalities (1992)

Noor, Muhammad Aslam

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 29-41. Published 1992 Jan 01. doi: 10.1155/s1048953392000030.

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Publication Date: 1992-01-01

Description: The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related to odd order boundary value problems, and to suggest a general algorithm. We also study the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique. Several special cases are discussed, which can be obtained from our results.

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41

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An existence theorem for differential inclusions on Banach space (1992)

Ahmed, N. U.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(2): 123-129. Published 1992 Jan 01. doi: 10.1155/s1048953392000091.

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Publication Date: 1992-01-01

Description: In this paper we consider the question of existence of solutions for a large class of nonlinear differential inclusions on Banach space arising from control theory.

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42

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Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations (1992)

Jackson, Dennis E.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 19-27. Published 1992 Jan 01. doi: 10.1155/s1048953392000029.

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Publication Date: 1992-01-01

Description: Existence and uniqueness are proved for nonlocal (in time) for solutions of linear parabolic partial differential equations. Instead of an initial condition, there is a relation connecting the initial value to values of the solution at other times. L2 error estimates are obtained for the semidiscrete approximation of the problem using finite elements in the space variables.

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On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities (1992)

Heikkilä, S. ; Kumpulainen, M. ; Lakshmikantham, V.

Hindawi

In: Journal of Applied Mathematics and Stochastic Analysis. 1992; 5(1): 1-17. Published 1992 Jan 01. doi: 10.1155/s1048953392000017.

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Publication Date: 1992-01-01

Description: In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence of coupled extremal quasisolutions of the systems of first and second order mixed quasimonotone differential equations with discontinuous right hand sides. Most of the results deal with systems in a Banach space ordered by a regular order cone.

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