Mathematical and asymptotic analysis of thermoelastic shells in normal damped response contact

CAO-RIAL, M.T.; CASTIÑEIRA, G.; RODRÍGUEZ-ARÓS, Á.; ROSCANI, S.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

ELSEVIER SCIENCE BV

Año: 2021 vol. 103

1007-5704

The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.