Geodesic
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 273-286 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
@article{CMJ_2006_56_2_a0,
     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},
     year = {2006},
     volume = {56},
     number = {2},
     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/