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

Voir la notice de l'article dans Czech Digital Mathematics Library

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
Mots-clés : 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},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2006},
     mrnumber = {2291736},
     zbl = {1164.35445},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_2_a0/}
}
TY  - JOUR
AU  - Park, Jong Yeoul
AU  - Park, Sun Hye
TI  - Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 273
EP  - 286
VL  - 56
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_2_a0/
LA  - en
ID  - CMJ_2006__56_2_a0
ER  - 
%0 Journal Article
%A Park, Jong Yeoul
%A Park, Sun Hye
%T Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
%J Czechoslovak Mathematical Journal
%D 2006
%P 273-286
%V 56
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_2_a0/
%G en
%F CMJ_2006__56_2_a0
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. https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_2_a0/