Stability analysis for a class of semilinear nonlocal evolution equations

被引：1

作者：

Van Loi, Do ^{[1
]}

Van Tuan, Tran ^{[2
]}

机构：

[1] Hongduc Univ, Dept Math, Thanhhoa, Vietnam

[2] Hanoi Pedag Univ 2, Dept Math, Phuc Yen, Vinh Phuc, Vietnam

来源：

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2023年 / 29卷 / 02期

关键词：

Nonlocal PDE; Stability; Weak stability; DIFFUSION;

D O I：

10.1007/s40590-023-00517-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our aim is to analyze some sufficient conditions ensuring the global solvability and stability of solutions to a class of nonlocal partial differential equations with nonlinear term, which describes numerous processes involving memory. By using the theory of completely positive functions, local estimates and fixed point arguments, we obtain some results on asymptotic stability and existence of decay solutions to our problem.

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页数：22

相关论文

共 19 条

[1] An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid [J].

Bazhlekova, Emilia ;

Jin, Bangti ;

Lazarov, Raytcho ;

Zhou, Zhi .

NUMERISCHE MATHEMATIK, 2015, 131 (01) :1-31

[2] Optimal control for evolution equations with memory [J].

Cannarsa, P. ;

Frankowska, H. ;

Marchini, E. M. .

JOURNAL OF EVOLUTION EQUATIONS, 2013, 13 (01) :197-227

[3] A PRIORI L2 ERROR-ESTIMATES FOR FINITE-ELEMENT METHODS FOR NONLINEAR DIFFUSION-EQUATIONS WITH MEMORY [J].

CANNON, JR ;

LIN, YP .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (03) :595-607

[4] ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF NON-LINEAR VOLTERRA-EQUATIONS WITH COMPLETELY POSITIVE KERNELS [J].

CLEMENT, P ;

NOHEL, JA .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1981, 12 (04) :514-535

[5]

Conti M, 2014, T AM MATH SOC, V366, P4969

[6]

Di Blasio G., 1994, J INTEGRAL EQUAT, V6, P479, DOI 10.1216/jiea/1181075833

[7]

Dr┬u├bek P., 2007, METHODS NONLINEAR AN

[8]

Evans LC., 2010, Partial Differential Equations, V2

[9] Existence results for some nonlocal partial integrodifferential equations without compactness or equicontinuity [J].

Ezzinbi, Khalil ;

Ghnimi, Saifeddine ;

Taoudi, Mohamed-Aziz .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (02)

[10]

Kamenskii M., 2001, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, DOI 10.1515/9783110870893