Integro-differential equations of hyperbolic type with positive definite kernels

被引：49

作者：

Cannarsa, Piermarco ^{[1
]}

Sforza, Daniela ^{[2
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, Sez Matemat, I-00161 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 250卷 / 12期

关键词：

Integro-differential equations; Global existence; Stability; Exponential decay; Weakly singular kernels; CONCENTRATED POLYMER SYSTEMS; DIFFERENTIAL-EQUATION; ASYMPTOTIC STABILITY; VOLTERRA EQUATION; VISCOELASTIC EQUATION; GLOBAL EXISTENCE; MEMORY; DECAY; DYNAMICS; BEHAVIOR;

D O I：

10.1016/j.jde.2011.03.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in Hilbert spaces. For kernels that decay exponentially at infinity and possess strongly positive definite primitives, the exponential stability of weak solutions is obtained in the energy norm. It is also shown that this theory applies to several examples of kernels with possibly variable sign, and to a problem in nonlinear viscoelasticity. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：4289 / 4335

页数：47

共 37 条

[1] Decay estimates for second order evolution equations with memory [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco ;

Sforza, Daniela .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (05) :1342-1372

[2] Exponential and polynomial stability of a wave equation for boundary memory damping with singular kernels [J].

Alabau-Boussouira, Fatiha ;

Pruess, Jan ;

Zacher, Rico .

COMPTES RENDUS MATHEMATIQUE, 2009, 347 (5-6) :277-282

[3]

Andrade D, 2006, J COMPUT ANAL APPL, V8, P173

[4]

[Anonymous], 1990, ENCY MATH APPL

[5]

[Anonymous], Q APPL MATH

[6] STRONGLY CONTINUOUS SEMIGROUPS, WEAK SOLUTIONS, AND VARIATION OF CONSTANTS FORMULA [J].

BALL, JM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 63 (02) :370-373

[7]

Baretto R., 1996, J ELASTICITY, V44, P61, DOI DOI 10.1007/BF00042192

[8] Existence and decay of solutions of a viscoelastic equation with a nonlinear source [J].

Berrimi, S ;

Messaoudi, SA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (10) :2314-2331

[9] Global solutions of abstract semilinear parabolic equations with memory terms [J].

Cannarsa, P ;

Sforza, D .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2003, 10 (04) :399-430

[10]

CANNARSA P, 2002, SERIES ADV MATH APPL, V62, P343

← 1 2 3 4 →