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In this article we study the hyperbolic problem (1) where Ω is a bounded region in R n whose boundary is partitioned into disjoint sets Γ0, Γ1. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the relaxation function.

Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type