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Initial-boundary value problems in elasticity. (English) Zbl 0686.73006
Ordinary and partial differential equations, Vol. II, Proc. 10th Dundee Conf., Dundee/UK 1988, Pitman Res. Notes Math. Ser. 216, 73-96 (1989).
[For the entire collection see Zbl 0673.00011.]
We start by treating initial-boundary value problems of linear elasticity, and indicate the existence of wave operators. The main part of the lecture is concerned with linear thermoelasticity. We solve initial-boundary value problems, give some asymptotic expansions as \(t\to \infty\), and especially describe the asymptotic behaviour of solutions of the free-space problem. Finally, we deal with some nonlinear questions. We are particularly interested in obtaining solutions global in t for small smooth data.

MSC:
74F05 Thermal effects in solid mechanics
35A15 Variational methods applied to PDEs
35C20 Asymptotic expansions of solutions to PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
35L05 Wave equation
35B40 Asymptotic behavior of solutions to PDEs