Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

doi:10.3969/j.issn.1000-5641.2019.03.003

Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (3): 13-23.doi: 10.3969/j.issn.1000-5641.2019.03.003

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Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

WANG Xuan, ZHAO Tao, ZHANG Yu-bao

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2018-04-02 Online:2019-05-25 Published:2019-05-30

Abstract

Abstract: In this paper, we study the asymptotic behavior of solutions for the classical reaction-diffusion equation with memory. Through the use of abstract function theory and semigroup theory, the existence of a global attractor in L²(Ω)×L_μ²(R⁺; H¹(Ω)) is proven when the internal nonlinearity and boundary nonlinearity adhere to polynomial growth of arbitrary order as well as the balance condition. This result extends and improves some known results.

Key words: classical reaction-diffusion equation, nonlinear boundary, fading memory, polynomial growth of arbitrary order

CLC Number:

O175.29

WANG Xuan, ZHAO Tao, ZHANG Yu-bao. Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 13-23.

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Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

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