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

Author(s)

Bezerra, F. D. M. ^[1] ; Nascimento, M. J. D. ^[2] ; da Silva, S. H. ^[3]

Affiliation

^[1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil

^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[3] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58051900 Campina Grande, PB - Brazil

• Document type: Journal article
• Source: MATHEMATICAL METHODS IN THE APPLIED SCIENCES; v. 38, n. 17, p. 4317-4329, NOV 30 2015.
• Web of Science Citations: 0

Abstract

where Omega is a bounded smooth domain in R-N, N >= 1, beta 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) := f(RN) J(x,y)u(y)dy, being J a non-negative function continuously differentiable on R-N x R-N and f(RN) J(, 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. is small enough, we show that the origin is locally pullback asymptotically stable. Copyright (C) 2014 John Wiley \& Sons, Ltd. (AU)

• FAPESP's process: 11/04166-5 - Continuity of attractors to parabolic problems
• Grantee: Marcelo José Dias Nascimento
• Support Opportunities: Regular Research Grants