Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

被引：4

作者：

Diop, Mamadou Abdoul ^{[1
]}

Caraballo, Tomas ^{[2
]}

Zene, Mahamat Mahamat ^{[1
]}

机构：

[1] Univ Gaston Berger, UFR Sci Appl & Technol, BP234, St Louis, Senegal

[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, E-41080 Seville, Spain

来源：

STOCHASTICS AND DYNAMICS | 2016年 / 16卷 / 06期

关键词：

Resolvent operators; C-0-semigroup; neutral stochastic partial integrodifferential equations; Wiener process; infinite delay; mild solutions; exponential stability; PARTIAL-DIFFERENTIAL-EQUATIONS; EXPONENTIAL STABILITY; FIXED-POINTS; EVOLUTION-EQUATIONS; MILD SOLUTIONS; ATTRACTORS;

D O I：

10.1142/S0219493716500143

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial integrodifferential equations with infinite delays. To prove the results, we use the theory of resolvent operators as developed by R. Grimmer [13], as well as a version of the fixed point principle. We establish sufficient conditions ensuring that the mild solutions are exponentially stable in pth-moment. An example is provided to illustrate the abstract results.

引用

页数：17

共 29 条

[1] Fixed points, stability, and exact linearization [J].

Burton, TA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (05) :857-870

[2] Fixed points and stability of an integral equation: Nonuniqueness [J].

Burton, TA ;

Zhang, B .

APPLIED MATHEMATICS LETTERS, 2004, 17 (07) :839-846

[3]

Burton TA, 2002, DYN SYST APPL, V11, P499

[4] Exponential stability of mild solutions of stochastic partial differential equations with delays [J].

Caraballo, T ;

Liu, K .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (05) :743-763

[5]

Caraballo T, 2007, DISCRETE CONT DYN-A, V18, P253

[6] Autonomous and non-autonomous attractors for differential equations with delays [J].

Caraballo, T ;

Marín-Rubio, P ;

Valero, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 208 (01) :9-41

[7] Attractors for 2D-Navier-Stokes models with delays [J].

Caraballo, T ;

Real, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 205 (02) :271-297

[8] The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion [J].

Caraballo, T. ;

Garrido-Atienza, M. J. ;

Taniguchi, T. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3671-3684

[9] PARTIAL-DIFFERENTIAL EQUATIONS WITH DELAYED RANDOM PERTURBATIONS - EXISTENCE, UNIQUENESS, AND STABILITY OF SOLUTIONS [J].

CARABALLO, T ;

REAL, J .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1993, 11 (05) :497-511

[10] CONTROL AND STABILIZATION FOR THE WAVE-EQUATION IN A BOUNDED DOMAIN [J].

CHEN, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1979, 17 (01) :66-81

← 1 2 3 →