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

WANG Xuan; ZHAO Tao; ZHANG Yu-bao

doi:10.3969/j.issn.1000-5641.2019.03.003

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May 2019

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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 Sciences), 2019, (3): 13-23. doi: 10.3969/j.issn.1000-5641.2019.03.003

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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 Sciences), 2019, (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

doi: 10.3969/j.issn.1000-5641.2019.03.003

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

Received Date: 2018-04-02
Publish Date: 2019-05-25

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 ${L^2}\left( \Omega \right) \times L_\mu ^2\left( {{\mathbb{R}^ + };{H^1}\left( \Omega \right)} \right)$ 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.
- classical reaction-diffusion equation,
- nonlinear boundary,
- fading memory,
- polynomial growth of arbitrary order

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References

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