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  • Articles  (932)
  • Numerical Methods and Modeling  (932)
  • Mathematics  (932)
  • Technology  (621)
  • 1
    Electronic Resource
    Electronic Resource
    Decay Estimates for Solutions of Linear Elasticity for Anisotropic Media (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to Lp-Lq-estimates.
    Additional Material: 4 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Multidimensional Oscillations for Non-linear Hyperbolic Mixed Problem: The Justified Non-linear Geometric Optics Method (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.
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  • 3
    Electronic Resource
    Electronic Resource
    The Child-Langmuir Asymptotics of the Vlasov-Poisson Equation for Cylindrically or Spherically Symmetric Diodes Part 2: Analysis of the Reduced Problem and Determination of the Child-Langmuir Current (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 313-340 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poisson problem in cylindrical or spherical symmetry. The problem was stated in the first part of this paper [2]. We recall that the Child-Langmuir asymptotics concerns the boundary value problem for the Vlasov-Poisson system in the situation where the thermal energy of the injected particles at the boundary is small compared with the external applied bias.In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or ‘reduced’) problem, which leads us to a characterization of the limit or ‘Child-Langmuir’ current which flows through the system.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Lyapunov Stability of a Class of Operator Integro-differential Equations with Applications to Viscoelasticity (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.
    Additional Material: 5 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chemical Reactor Dynamics: Stability of Steady States (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations describing the dynamics and steady states of a tubular reactor are studied in the region where an arbitrary number of steady-state solutions exist. The stability of these solutions is examined and their persistence for increases in the parameter values is determined. The physical implications of these solutions are examined.
    Additional Material: 3 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Heteroclinic Solutions for a System of Strongly Coupled ODEs (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.
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  • 7
    Electronic Resource
    Electronic Resource
    Semi-internal Stabilization for a Non-linear Bernoulli-Euler Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.
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  • 8
    Electronic Resource
    Electronic Resource
    Local Solutions of Semilinear Wave Equations in Hs+1 (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 145-170 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for the wave equation with power type non-linearity ±∣u∣σ*u and data in Hs+1(∝n)×Hs(∝n) is considered, where 0〈s〈(n/2)-1 and n≥3. Under the growth restriction σ*≤4/(n-2-2s) in many cases the existence of a local solution with u(t)∊Hs+1(∝n) is shown which is unique in a closely related class.
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  • 9
    Electronic Resource
    Electronic Resource
    Measure-valued Solutions of the Euler Equations for Ideal Compressible Polytropic Fluids (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 235-252 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global measure-valued solutions to the Euler equations describing the motion of an ideal compressible and heat conducting fluid is proved. The motion is considered in a bounded domain Ω⊂∝3 with impermeable boundary. The solution is a limit of an approximate solution obtained by adding the sixth-order elliptic operator in the equation of momentum.
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  • 10
    Electronic Resource
    Electronic Resource
    Hadamard's Finite Part (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1017-1052 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A systematic way of ascribing values to integrals which diverge at infinity is described. For integrals with algebraic or logarithmic behaviour it is akin to Hadamard's finite part for integrands which have singularities at finite points. The power of the method is illustrated by examples of particular integrals and the convolution of distributions which are beyond the range of standard theory. Both one-dimensional and multi-dimensional integrals are included. The theory also enables the definition of products of distributions which are considered normally to be too singular for multiplication.
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