Hopf bifurcation in a reaction-diffusion-advection model with nonlocal delay effect and Dirichlet boundary condition
type: Item
instance of: scholarly article
title: Hopf bifurcation in a reaction-diffusion-advection model with nonlocal delay effect and Dirichlet boundary condition
zbMATH Open document ID: 1503.35027
author: Tingting Wen
author: Xiaoli Wang
author: Guohong Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2022-11-28T00:00:00Z
review text: In this paper, the authors follows the approach by \textit{S. Guo} [J. Differ. Equations 259, No. 4, 1409--1448 (2015; Zbl 1323.35082)] and obtain the existence of the spatially nonhomogeneous steady-state solutions of a delayed reaction-diffusion-advection model by using the Lyapunov-Schmidt reduction. The associated eigenvalue problem is investigated and the existence of the Hopf bifurcation near the spatially nonhomogeneous steady states is obtained as well. In particular, the direction of the Hopf bifurcation and the stability of bifurcating periodic orbits are obtained. Finally, some applications and simulations are given to verify the theoretical results.
reviewed by: Shangjiang Guo
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 7624116
zbMATH Keywords: reaction-diffusion-advection equation
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: nonlocal delay
zbMATH Keywords: Hopf bifurcation
Wikidata QID: Q123267622
MaRDI profile type: Publication
full work available at URL: j.jmaa.2022.126823
OpenAlex ID: W4307483137
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DOI: 10.1016/J.JMAA.2022.126823
description: scientific article; zbMATH DE number 7624116