带有非线性边界条件的弱记忆型经典反应扩散方程解的渐近性

Journal of Jilin University Science Edition ›› 2019, Vol. 57 ›› Issue (5): 1028-1034.

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Asymptotic Behavior of Solutions for Classical ReactionDiffusionEquation with Nonlinear Boundary Condition and Weak Memory#br#

ZHAO Tao, WANG Xuan

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

Received:2018-09-29 Online:2019-09-26 Published:2019-09-17
Contact: WANG Xuan E-mail:wangxuan@nwnu.edu.cn

Abstract

Abstract: We considered the asymptotic behavior of solutions for the classical reactiondiffusion equation with weak memory. When the internal and boundary nonlinearities adhered to supercritical exponential growth and the equilibrium condition, we proved the existence of a global attractor in L²(Ω)×L²_μ(R+;L²(Ω)) by using contractive function method and semigroup theory.

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

CLC Number:

O175.29

ZHAO Tao, WANG Xuan. Asymptotic Behavior of Solutions for Classical ReactionDiffusionEquation with Nonlinear Boundary Condition and Weak Memory#br#[J].Journal of Jilin University Science Edition, 2019, 57(5): 1028-1034.

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Asymptotic Behavior of Solutions for Classical ReactionDiffusionEquation with Nonlinear Boundary Condition and Weak Memory#br#

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