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

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

Congreso; Mathematical Congress of the Americas; 2021

We consider a dynamic contact problem in thermoelasticity, where 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 we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.