Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park; Sun Hye Park

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 273-286
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Park, Jong Yeoul, and Park, Sun Hye. "Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation." Czechoslovak Mathematical Journal 56.2 (2006): 273-286. <http://eudml.org/doc/31028>.

@article{Park2006,
abstract = {We consider the damped semilinear viscoelastic wave equation \[ u^\{\prime \prime \} - \Delta u + \int ^t\_0 h (t-\tau ) \operatorname\{div\}\lbrace a \nabla u(\tau ) \rbrace \mathrm \{d\}\tau + g(u^\{\prime \}) = 0 \quad \text\{in\}\hspace\{5.0pt\}\Omega \times (0,\infty ) \] 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.},
author = {Park, Jong Yeoul, Park, Sun Hye},
journal = {Czechoslovak Mathematical Journal},
keywords = {asymptotic stability; viscoelastic problems; boundary dissipation; wave equation; asymptotic stability; viscoelastic problems; boundary dissipation; wave equation},
language = {eng},
number = {2},
pages = {273-286},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation},
url = {http://eudml.org/doc/31028},
volume = {56},
year = {2006},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 273
EP - 286
AB - We consider the damped semilinear viscoelastic wave equation \[ u^{\prime \prime } - \Delta u + \int ^t_0 h (t-\tau ) \operatorname{div}\lbrace a \nabla u(\tau ) \rbrace \mathrm {d}\tau + g(u^{\prime }) = 0 \quad \text{in}\hspace{5.0pt}\Omega \times (0,\infty ) \] 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.
LA - eng
KW - asymptotic stability; viscoelastic problems; boundary dissipation; wave equation; asymptotic stability; viscoelastic problems; boundary dissipation; wave equation
UR - http://eudml.org/doc/31028
ER -

References

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