p th Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

Xiongrui Wang, Ruofeng Rao and Shouming Zhong
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Xiongrui Wang: College of Mathematics, Yibin University, Yibin 644000, China
Ruofeng Rao: Department of Mathematics, Chengdu Normal University, Chengdu 611130, China
Shouming Zhong: College of mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China

Mathematics, 2020, vol. 8, issue 2, 1-10

Abstract: In this paper, the Sobolev embedding theorem, Holder inequality, the Lebesgue contrl convergence theorem, the operator norm estimation technique, and critical point theory are employed to prove the existence of nontrivial stationary solution for p -Laplacian diffusion system with distributed delays. Furthermore, by giving the definition of p th moment stability, the authors use the Lyapunovfunctional method and Kamke function to derive the stability of nontrivialstationary solution. Moreover, a numerical example illuminates the effectiveness of the proposed methods. Finally, an interesting further thought is put forward, which is conducive to the in-depth study of the problem.

Keywords: large-scale variational methods; Lyapunovfunctional; p th moment stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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