Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems

Autor(es)

Alves, M. S. ^[1] ; Jorge Silva, M. A. ^[2] ; Ma, T. F. ^[3] ; Munoz Rivera, J. E. ^{[4, 5]}

Afiliação do(s) autor(es)

^[1] Univ Fed Vicosa, Dept Math, BR-36570000 Vicosa, MG - Brazil

^[2] Univ Estadual Londrina, Dept Math, BR-86057970 Londrina, PR - Brazil

^[3] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil

^[4] Natl Lab Sci Computat, BR-25651070 Petropolis, RJ - Brazil

^[5] Univ Fed Rio de Janeiro, Inst Math, BR-21941909 Rio De Janeiro, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK; v. 67, n. 3 JUN 2016.
• Citações Web of Science: 1

Resumo

This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Junior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate t(-1/2) for mixed Dirichlet-Neumann boundary condition and rate t(-1/4) for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate t(-1/2) (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems. (AU)

• Processo FAPESP: 12/19274-0 - Dinâmica assintótica de equações de ondas não lineares e não autônomas
• Beneficiário: Ma To Fu
• Modalidade de apoio: Auxílio à Pesquisa - Regular