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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
Pedro Roberto de Lima 1,, and Hugo D. Fernández Sare 2,
Departamento de Matemática, Universidade Estadual do Centro-Oeste, Guarapuava, PR, CEP 85040-167, Brazil
Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, CEP 36036-900, Brazil
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.
Keywords: Bresse system, exponential Stability, Cattaneo's law.
Mathematics Subject Classification: Primary: 35B40, 35E15, 35Q74; Secondary: 74B05, 74F05.
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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Pedro Roberto de Lima Hugo D. Fernández Sare