Existence and asymptotic stability for viscoelastic evolution problems on compact manifolds, part II

被引：0

作者：

Andrade, D ^{[1
]}

Cavalcanti, MM

Cavalcanti, VND

Oquendo, HP

机构：

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

[2] Univ Fed Parana, Dept Matemat, BR-81531900 Curibata, PR, Brazil

来源：

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS | 2006年 / 8卷 / 03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：

The present paper makes a further study on the existence and stabilization in a earlier article (J. Concr. Appl. Math). One considers the nonlinear viscoelastic evolution equation u(tt) + Au + F(x,t,u,u(t)) - g* A u = 0 on Gamma x (0, infinity) where Gamma is a compact manifold. When F not equal 0 and g not equal 0 we prove existence of global solutions as well as uniform (exponential and algebraic) decay rates, provided the kernel of the memory decays exponentially and F satisfies suitable growth assumptions.

引用

页码：287 / 301

页数：15

共 47 条

[1] Existence and asymptotic stability for viscoelastic evolution problems on compact manifolds
Andrade, D
Cavalcanti, MA
Cavalcanti, VND
Oquendo, HP
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2006, 8 (02) : 173 - 193
[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 →