Decay rates for solutions of a Timoshenko system with a memory condition at the boundary. (English) Zbl 1011.35094

De Lima Santos, Mauro

Abstr. Appl. Anal. 7, No. 10, 531-546 (2002).

This paper is very interesting. The author considers a Timoshenko system with memory condition at the boundary and he studies in an elegant way the asymptotic behavior of the corresponding solutions. He proves that the energy decays with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially using the famous Volterra operator.

Reviewer: Jorge Ferreira (Maringá-Paraná)

MSC:

35L70	Second-order nonlinear hyperbolic equations
35B40	Asymptotic behavior of solutions to PDEs
35L20	Initial-boundary value problems for second-order hyperbolic equations

Keywords:

exponential decay; polynomial decay; relaxation functions