Existence and asymptotic stability for viscoelastic evolution problems on compact manifolds

被引：0

作者：

Andrade, D ^{[1
]}

Cavalcanti, MA

Cavalcanti, VND

Oquendo, HP

机构：

[1] Univ Estadual Maringa, Dept Matemat, BR-87020900 Maringa, Parana, Brazil

[2] Univ Fed Parana, Dept Matemat, BR-81531990 Curitiba, Parana, Brazil

来源：

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS | 2006年 / 8卷 / 02期

关键词：

asymptotic stability; viscoelastic evolution problem;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

One considers the nonlinear viscoelastic evolution equation u(tt) + Au + F(x,t,u,u(t)) - g * Au = 0 on Gamma x (0, infinity) where Gamma is a compact manifold. When F not equal 0 and g = 0 we prove existence of global solutions as well as uniform (exponential and algebraic) decay rates. Furthermore, if F = 0 and g not equal 0 we prove that the dissipation introduced by the memory effect is strong enough to allow us to derive an exponential( or polynornial) decay rate provided the resolvent kernel of the relaxation function decays exponentially (or polynomially).

引用

页码：173 / 193

页数：21

共 50 条

[1] Existence and asymptotic stability for viscoelastic evolution problems on compact manifolds, part II
Andrade, D
Cavalcanti, MM
Cavalcanti, VND
Oquendo, HP
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2006, 8 (03) : 287 - 301
[2] Existence and asymptotic stability for evolution problems on manifolds with damping and source terms
Cavalcanti, MM
Cavalcanti, VND
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 291 (01) : 109 - 127
[3] Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
Jong Yeoul Park
Sun Hye Park
[J]. Czechoslovak Mathematical Journal, 2006, 56 : 273 - 286
[4] Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
Park, Jong Yeoul
Park, Sun Hye
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2006, 56 (02) : 273 - 286
[5] ASYMPTOTIC STABILITY OF THE WAVE EQUATION ON COMPACT MANIFOLDS AND LOCALLY DISTRIBUTED VISCOELASTIC DISSIPATION
Cavalcanti, Marcelo M.
Domingos Cavalcanti, Valeria N.
Nascimento, Flavio A. F.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (09) : 3183 - 3193
[6] Existence and asymptotic stability for the wave equation on compact manifolds with nonlinearities of arbitrary growth
Cavalcanti, Marcelo M.
Cavalcanti, Valeria N. Domingos
Antunes, Jose Guilherme Simion
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 248
[7] Existence and asymptotic stability of a viscoelastic wave equation with a delay
Kirane, Mokhtar
Said-Houari, Belkacem
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (06): : 1065 - 1082
[8] ON THE EXISTENCE AND THE ASYMPTOTIC STABILITY OF SOLUTIONS FOR LINEARLY VISCOELASTIC SOLIDS
FABRIZIO, M
LAZZARI, B
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 116 (02) : 139 - 152
[9] Existence and asymptotic stability of a viscoelastic wave equation with a delay
Mokhtar Kirane
Belkacem Said-Houari
[J]. Zeitschrift für angewandte Mathematik und Physik, 2011, 62 : 1065 - 1082
[10] ASYMPTOTIC STABILITY OF THE WAVE EQUATION ON COMPACT MANIFOLDS AND LOCALLY DISTRIBUTED VISCOELASTIC DISSIPATION (vol 141, pg 3183, 2013)
Cavalcanti, M. M.
Domingos Cavalcanti, V. N.
Falcao Nascimento, F. A.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (09) : 4097 - 4097

← 1 2 3 4 5 →