Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions

Jihoon Lee; Vu Manh Toi

doi:10.3934/dcdsb.2020054

Article Contents

2020, Volume 25, Issue 8: 3135-3152. Doi: 10.3934/dcdsb.2020054

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Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions

Jihoon Lee^1, and
Vu Manh Toi^2, ,

1.
Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Korea
2.
Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam

^* Corresponding author: Vu Manh Toi
^* Corresponding author: Vu Manh Toi

Received: May 2019

Revised: October 2019

Early access: February 2020

Published: August 2020

The first author is supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1A6A3A01091340). The second author is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.303

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Abstract

In this paper we study the asymptotic behavior of solutions for a class of nonautonomous reaction-diffusion equations with dynamic boundary conditions possessing finite delay. Under the polynomial conditions of reaction term, suitable conditions of delay terms and a minimal conditions of time-dependent force functions, we first prove the existence and uniqueness of solutions by using the Galerkin method. Then, we ensure the existence of pullback attractors for the associated process to the problem by proving some uniform estimates and asymptotic compactness properties (via an energy method). With an additional condition of time-dependent force functions, we prove that the boundedness of pullback attractors in smoother spaces.

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Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 65Mxx, 35A01.

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