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  • Artikel  (12)
  • Mathematics and Statistics  (12)
  • AERODYNAMICS
  • Cell & Developmental Biology
  • Life and Medical Sciences
  • Polymer and Materials Science
  • 1990-1994  (8)
  • 1980-1984  (4)
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  • 1915-1919
  • 1890-1899
  • 1994  (8)
  • 1984  (4)
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  • Mathematik  (12)
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  • Artikel  (12)
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  • 1990-1994  (8)
  • 1980-1984  (4)
  • 1940-1944
  • 1915-1919
  • 1890-1899
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  • 1
    Digitale Medien
    Digitale Medien
    Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita-type systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1005-1016 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita-type systems are considered leading to global existence and finite time blow-up results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670171302
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  • 2
    Digitale Medien
    Digitale Medien
    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060104
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  • 3
    Digitale Medien
    Digitale Medien
    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060129
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  • 4
    Digitale Medien
    Digitale Medien
    Thin elastic and periodic plates (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 159-191 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060112
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  • 5
    Digitale Medien
    Digitale Medien
    Numerical Computation of Waves at High Frequencies by an Iterated WKB-Method (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 520-526 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An integral operator is defined, which allows to solve the equation by Neumann series for sufficiently large k 〉 0. The kernel is constructed by a modification of the WKB-method. This kernel is so simple that the operator can be used effectively for numerical calculations. Numerical results are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060133
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  • 6
    Digitale Medien
    Digitale Medien
    A tracking method for gas flow into vacuum based on the vacuum Riemann problem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 597-612 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, a tracking method is proposed for the expansion of gas flow into vacuum which may be combined with numerical methods for the equations of gas dynamics, the Euler equations. This tracking prevents the difficulties of the numerical approximation introduced by the vacuum as a region where the Euler equations are not valid due to the failure of the continuum assumption. The tracking algorithm is based on the exact or an approximate solution of the vacuum Riemann problem. This is the initial value problem with two constant states, one being the gas and the other the vacuum state, and a limit case of the usual Riemann problem. In this approach, the gas-vacuum boundary is sharply resolved within one mesh interval. For a test problem, the numerical results of gas flow into vacuum are presented which indicate that the gas vacuum boundary is captured very well.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670170803
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  • 7
    Digitale Medien
    Digitale Medien
    Regularity of solutions and approximate inertial manifolds for von Karman evolution equations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 667-680 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The necessary and sufficient conditions of regularity of solutions of von Karman evolution equations are derived. It is proved that a global attractor consists of smooth functions for these evolution equations. The results obtained are used to construct a family of approximate inertial manifolds. These finite dimensional manifolds approximate the global attractor and are determined by a simple iterative procedure. Their use makes it possible to suggest a new method of numerical investigation of long-time behaviour and limit regimes of the equations in question. In particular, this method can be applied for studying a non-linear flutter problem in real air space systems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670170902
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  • 8
    Digitale Medien
    Digitale Medien
    Approximation of solutions to evolution equations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 753-763 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form u′(t)= - Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self-adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non-linear map defined on D(A½) which satisfies a Lipschitz condition on balls in D(A½).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670171002
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  • 9
    Digitale Medien
    Digitale Medien
    Dynamical stability of an elastic column and the phenomenon of bifurcation (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 855-875 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The article studies the stability of rectilinear equilibrium shapes of a non-linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6] solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite-dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite-dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post-buckling).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670171103
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  • 10
    Digitale Medien
    Digitale Medien
    Numerical analysis of semi-linear parabolic systems in diffusion-reaction problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 41-69 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we investigate problems of approximation for the solution of a system of coupled semi-linear parabolic partial differential equations that model diffusion-reaction problems in chemical engineering. Given that the solutions belong to Hs (0, ∞), we consider finite-element approximations on bounded domains (0, R(h)) such that limh→0[R(h)] = ∞. Optimal convergence estimates are found to depend on the asymptotic behaviour of the solution and its regularity near t = 0. In the L2-norm, they cannot exceed an order of O((;h2/t3/4) + h2[In h]2). For that purpose, a Wheeler-type argument is also generalized to non-coercive elliptic forms. Fully discrete schemes that preserve the positivity of the solutions are also considered. Due to the singularity at t = 0, they lead to estimates of the order O(τ1/4 + h2/t3/4).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670170105
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