# Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Czechoslovak Mathematical Journal (2006)

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

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topPark, 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 -

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