de Lima Santos, Mauro Decay rates for solutions of a system of wave equations with memory. (English) Zbl 1010.35012 Electron. J. Differ. Equ. 2002, Paper No. 38, 17 p. (2002). The author considers the initial-boundary value problem for the system \[ u_{tt}-\Delta u+\int^t_0 g_1(t-s)\Delta u(s)ds+ \alpha\cdot(u-v)=0\quad\text{in }\Omega \times(0,\infty) \]\[ v_{tt}-\Delta v+\int^t_0 g_2(t-s)\Delta v(s) ds-\alpha\cdot(u-v)=0\quad\text{in }\Omega\times(0,\infty) \] with homogeneous Dirichlet boundary condition, where \(\Omega\subset\mathbb{R}^n\) is a bounded domain. By using Galerkin approximations, it is proved the existence of a unique strong solution (in appropriate Sobolev spaces). Further, by using a Lyapunov functional, it is shown that the solution decays exponentially to zero provided \(g_i\) decays exponentially to zero. If \(g_i\) decays polynomially to zero then the solution also decays polynomially with the same rate of decay. Reviewer: László Simon (Budapest) Cited in 15 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35L55 Higher-order hyperbolic systems 35L20 Initial-boundary value problems for second-order hyperbolic equations Keywords:homogeneous Dirichlet boundary condition; Galerkin approximations; unique strong solution; Lyapunov functional PDFBibTeX XMLCite \textit{M. de Lima Santos}, Electron. J. Differ. Equ. 2002, Paper No. 38, 17 p. (2002; Zbl 1010.35012) Full Text: EuDML EMIS