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Decay rates for solutions of semilinear wave equations with a memory condition at the boundary

2002; University of Szeged; Issue: 7 Linguagem: Inglês

10.14232/ejqtde.2002.1.7

1417-3875

Mauro de Lima Santos,

Advanced Mathematical Physics Problems

In this paper, we study the stability of solutions for semilinear wave equations whose boundary condition includes an integral that represents the memory eect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.