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Numerical solution for the Cauchy problem in nonlinear 1-D- thermoelasticity. (English) Zbl 0701.73001
An initial problem of classical nonlinear one-dimensional coupled thermoelasticity on \({\mathbb{R}}^ 1\) is replaced by an adjacent initial- boundary value problem on the bounded interval (-R,R) with \(R>0\) sufficiently large and the boundary conditions in terms of a far field solution to the initial problem; and for the adjacent problem a numerical procedure is proposed. Convergence of the procedure is established and a numerical example is included. The physical motivation for a particular choice of the material functions in the numerical example is not given however.
Reviewer: J.Ignaczak

74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
74S20 Finite difference methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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