On the existence of patterns in reaction-diffusion problems with Dirichlet boundary conditions-Reference-Cited by-同舟云学术

On the existence of patterns in reaction-diffusion problems with Dirichlet boundary conditions

Published:2024 Issue:30 Volume: Page:1-14
ISSN:1417-3875
Container-title:Electronic Journal of Qualitative Theory of Differential Equations
language:en
Short-container-title:Electron. J. Qual. Theory Differ. Equ.

Author:

Sônego Maicon¹^ORCID

Affiliation:

1. Universidade Federal de Itajubá

Abstract

Consider a general reaction-diffusion problem, u t = Δ u + f ( x , u , u x ) , on a revolution surface or in an n -dimensional ball with Dirichlet boundary conditions. In this work, we provide conditions related to the geometry of the domain and the spatial heterogeneities of the problem that ensure the existence or not of a non-constant stationary stable solution. Several applications are presented, particularly with regard to the Allen–Cahn, Fisher–KPP and sine-Gordon equations.

Publisher

University of Szeged

Link

https://www.math.u-szeged.hu/ejqtde/p10827.pdf

Reference21 articles.

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