Feireisl, Eduard Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem. (English) Zbl 0718.73013 Commentat. Math. Univ. Carol. 31, No. 2, 243-255 (1990). 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. Reviewer: N.Sandru (Bucureşti) 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 Keywords:topological degree of mapping; Lebesgue space; Sobolev spaces of integrable functions; nonlinear operator equation; smooth time-periodic solutions; hyperbolic-parabolic system of equations; Galerkin approximation; finite system of nonlinear equations PDF BibTeX XML Cite \textit{E. Feireisl}, Commentat. Math. Univ. Carol. 31, No. 2, 243--255 (1990; Zbl 0718.73013) Full Text: EuDML