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Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul ParkSun Hye Park — 2006

Czechoslovak Mathematical Journal

We consider the damped semilinear viscoelastic wave equation u ' ' - Δ u + 0 t h ( t - τ ) div { a u ( τ ) } d τ + g ( u ' ) = 0 in Ω × ( 0 , ) with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.

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