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On the theoretical and numerical stability of the thermoviscoelastic Bresse system
Author(s) -
EL Arwadi Toufic,
Copetti Maria Inês M.,
Youssef Wael
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800207
Subject(s) - dissipation , generalization , beam (structure) , viscoelasticity , stability (learning theory) , timoshenko beam theory , space (punctuation) , exponential stability , mathematical analysis , energy (signal processing) , mathematics , exponential function , euler's formula , type (biology) , physics , classical mechanics , computer science , nonlinear system , optics , thermodynamics , statistics , quantum mechanics , machine learning , operating system , ecology , biology
Abstract In this paper, we shall study the stability of the Bresse system where the equations are damped by the dissipation from the viscoelasticity and the thermoelasticity. The thermoviscoelastic Bresse beam is a generalization of the thermoviscoelastic Timoshenko beam. Theoretically, we prove the exponential decay of the energy. Later, we introduce and study an implicit Euler type scheme based on finite differences in time and finite elements in space. We show that the discrete energy decreases in time and obtain error estimates. At the end, numerical simulations are presented.