Asymptotic behavior of solutions to a class of nonlocal non‐autonomous diffusion equations | Zendy

Bezerra F. D. M. | Zendy; Nascimento M. J. D. | Zendy; Silva S. H. | Zendy

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Asymptotic behavior of solutions to a class of nonlocal non‐autonomous diffusion equations

Author(s) -

Bezerra F. D. M.,

Nascimento M. J. D.,

Silva S. H.

Publication year - 2014

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.3369

Subject(s) - pullback attractor , mathematics , bounded function , differentiable function , constant (computer programming) , domain (mathematical analysis) , mathematical analysis , operator (biology) , pullback , kernel (algebra) , attractor , monotonic function , function (biology) , pure mathematics , biochemistry , chemistry , repressor , evolutionary biology , biology , computer science , transcription factor , gene , programming language

In this paper, we consider the nonlocal non‐autonomous evolution problems where Ω is a bounded smooth domain inR N , N ≥1, β is a positive constant, the coefficient a is a continuous bounded function on R , and K is an integral operator with symmetric kernel ( Ku ) ( x ) : = ∫R NJ ( x , y ) u ( y ) dy , being J a non‐negative function continuously differentiable onR N × R Nand∫R NJ ( · , y ) dy = 1 . We prove the existence of global pullback attractor, and we exhibit a functional to evolution process generated by this problem that decreases along of solutions. Assuming the parameter β is small enough, we show that the origin is locally pullback asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd.

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