Geodesic
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 273-286.

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We consider the damped semilinear viscoelastic wave equation \[ u^{\prime \prime } - \Delta u + \int ^t_0 h (t-\tau ) \div \lbrace a \nabla u(\tau ) \rbrace \mathrm{d}\tau + g(u^{\prime }) = 0 \quad \text{in}\hspace{5.0pt}\Omega \times (0,\infty ) \] 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.
Classification : 35B35, 35B40, 35L15, 35L70, 35Q72, 65M60, 74D10, 74H20
Keywords: asymptotic stability; viscoelastic problems; boundary dissipation; wave equation 
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     author = {Park, Jong Yeoul and Park, Sun Hye},
     title = {Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation},
     journal = {Czechoslovak Mathematical Journal},
     pages = {273--286},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2006},
     mrnumber = {2291736},
     zbl = {1164.35445},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a0/}
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Park, Jong Yeoul; Park, Sun Hye. Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 273-286. http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a0/