Mindlin-Timoshenko systems with Kelvin-Voigt: analyticity and optimal decay rates

Author(s)

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

Affiliation

^[1] Univ Estadual Londrina, Dept Matemat, BR-86057970 Londrina, PR - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil

^[3] Lab Nacl Computacao Cientif, BR-25651070 Petropolis, RJ - Brazil

^[4] Univ Fed Rio de Janeiro, Inst Matemat, BR-31941909 Rio De Janeiro - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 417, n. 1, p. 164-179, SEP 1 2014.
• Web of Science Citations: 4

Abstract

This paper is concerned with asymptotic stability of Mindlin-Timoshenko plates with dissipation of Kelvin-Voigt type on the equations for the rotation angles. We prove that the corresponding evolution semigroup is analytic if a viscoelastic damping is also effective over the equation for the transversal displacements. On the contrary, if the transversal displacement is undamped, we show that the semigroup is neither analytic nor exponentially stable. In addition, in the latter case, we show that the solution decays polynomially and we prove that the decay rate found is optimal. (C) 2014 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 08/00123-7 - Asymptotic stability of nonlocally defined evolution equations.
• Grantee: Marcio Antonio Jorge da Silva
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 12/19274-0 - Asymptotic dynamics for autonomous and nonautonomous nonlinear wave equations
• Grantee: Ma To Fu
• Support Opportunities: Regular Research Grants