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

Pedro Roberto de Lima; Hugo D. Fernández Sare

doi:10.3934/cpaa.2020156

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2020, Volume 19, Issue 7: 3575-3596. Doi: 10.3934/cpaa.2020156

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

Pedro Roberto de Lima^1, , and
Hugo D. Fernández Sare^2,

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
^*Corresponding author

Received: April 30, 2019

Revised: December 31, 2019

Published: April 2020

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35E15, 35Q74; Secondary: 74B05, 74F05.

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References

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