Asymptotic behavior of solutions to a class of nonlocal non‐autonomous diffusion equations |
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Authors: | F D M Bezerra M J D Nascimento S H da Silva |
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Institution: | 1. Departamento de Matemática, Universidade Federal da Paraíba, 58051‐900, Jo?o Pessoa ‐ PB, Brazil;2. Departamento de Matemática, Universidade Federal de S?o Carlos, 13565‐905 S?o Carlos ‐ SP, Brazil;3. Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58051‐900 Campina Grande ‐ PB, Brazil |
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Abstract: | In this paper, we consider the nonlocal non‐autonomous evolution problems where Ω is a bounded smooth domain in , N≥1, β is a positive constant, the coefficient a is a continuous bounded function on , and K is an integral operator with symmetric kernel , being J a non‐negative function continuously differentiable on and . 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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Keywords: | pullback attractors nonlocal diffusion equations non‐autonomous equations evolution process |
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