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Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

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Abstract

We consider the damped semilinear viscoelastic wave equation

$$u'' - \Delta u + \int_0^t h (t - \tau ) div\{ a\nabla u(\tau )\} d\tau + g(u') = 0 in \Omega \times (0,\infty )$$

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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Authors and Affiliations

  1. Department of Mathematics, Busan National University, Busan, 609-735, Korea

    Jong Yeoul Park & Sun Hye Park

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  1. Jong Yeoul Park
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  2. Sun Hye Park
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Park, J.Y., Park, S.H. Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation. Czech Math J 56, 273–286 (2006). https://doi.org/10.1007/s10587-006-0017-5

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  • DOI: https://doi.org/10.1007/s10587-006-0017-5

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