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Original Articles

Mathematical Analysis and Numerical Simulation of a Nonlinear Thermoelastic System

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Pages 1514-1542 | Received 20 Mar 2017, Accepted 06 Jun 2018, Published online: 05 Oct 2018
 

Abstract

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear non-local thermoelastic coupled system with linear boundary conditions. Furthermore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time which results in a nonlinear system to be solved by Newton’s method. Numerical experiments for one-dimensional and two-dimensional cases are presented in order to estimate the rate of convergence of the numerical solution that confirm our analysis and show the efficiency of the method.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Additional information

Funding

The author M.A. Rincon acknowledges the partial support for research from CNPq of Brazil.

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