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July  2020, 19(7): 3575-3596. doi: 10.3934/cpaa.2020156

## General condition for exponential stability of thermoelastic Bresse systems with Cattaneo's law

 1 Departamento de Matemática, Universidade Estadual do Centro-Oeste, Guarapuava, PR, CEP 85040-167, Brazil 2 Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, CEP 36036-900, Brazil

*Corresponding author

Received  May 2019 Revised  January 2020 Published  April 2020

Fund Project: The first author was supported by CAPES at the Instituto de Matemática of the Universidade Federal do Rio de Janeiro when this work was submitted

In this paper, we give a new and more general sufficient condition for exponential stability of thermoelastic Bresse systems with heat flux given by Cattaneo's law acting in shear and longitudinal motion equations. This condition, which we also prove to be necessary in some special cases, is given by a relation between the constants of the system and generalizes the well-known equal wave speed condition.

Citation: Pedro Roberto de Lima, Hugo D. Fernández Sare. General condition for exponential stability of thermoelastic Bresse systems with Cattaneo's law. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3575-3596. doi: 10.3934/cpaa.2020156
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