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2021, Volume 29, Issue 5: 3017-3030. doi: 10.3934/era.2021024
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Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect

  • School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 611756, China
  • Received: 01 December 2020 Revised: 01 February 2021 Published: 16 March 2021

  • Primary: 35A01, 35K55, 35K57, 92D25; Secondary: 35K57

  • This paper is devoted to studying the Cauchy problem corresponding to the nonlocal bistable reaction diffusion equation. It is the first attempt to use the method of comparison principle to study the well-posedness for the nonlocal bistable reaction-diffusion equation. We show that the problem has a unique solution for any non-negative bounded initial value by using Gronwall's inequality. Moreover, the boundedness of the solution is obtained by means of the auxiliary problem. Finally, in the case that the initial data with compactly supported, we analyze the asymptotic behavior of the solution.

    Citation: Meng-Xue Chang, Bang-Sheng Han, Xiao-Ming Fan. Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect[J]. Electronic Research Archive, 2021, 29(5): 3017-3030. doi: 10.3934/era.2021024

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  • This paper is devoted to studying the Cauchy problem corresponding to the nonlocal bistable reaction diffusion equation. It is the first attempt to use the method of comparison principle to study the well-posedness for the nonlocal bistable reaction-diffusion equation. We show that the problem has a unique solution for any non-negative bounded initial value by using Gronwall's inequality. Moreover, the boundedness of the solution is obtained by means of the auxiliary problem. Finally, in the case that the initial data with compactly supported, we analyze the asymptotic behavior of the solution.





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