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Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem. (English) Zbl 0718.73013
An existence theorem for smooth time-periodic solutions of the hyperbolic-parabolic system of equations of one-dimensional thermoelasticity is obtained. Using the technique of Galerkin approximation, the author reduces the problem to solving a sequence of a finite system of nonlinear equations. The main tool used for solving these nonlinear equations is a consequence of the Poincaré-Bohl theorem from the classical degree theory. To apply this result one needs some suitable a priori estimates.
MSC:
74A15 Thermodynamics in solid mechanics
35B10 Periodic solutions to PDEs
35Q72 Other PDE from mechanics (MSC2000)
35B45 A priori estimates in context of PDEs
74B10 Linear elasticity with initial stresses
74B20 Nonlinear elasticity
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