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

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.


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