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On a nonlinear thermoelastic system with nonlocal coefficients. (English) Zbl 1327.35071
Summary: This paper deals with the global existence and uniqueness of solutions, and uniform stabilization of the energy of an initial-boundary value problem for a thermoelastic system with nonlinear terms of nonlocal kind. The asymptotic stabilization of the energy of system is obtained without any dissipation mechanism acting in the displacement variable \(u\) of the membrane equation.

MSC:
35G61 Initial-boundary value problems for systems of nonlinear higher-order PDEs
74F05 Thermal effects in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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