Stability results for a reaction-diffusion problem with mixed boundary conditions and applications to some symmetric cases

被引：4

作者：

Sonego, Maicon ^{[1
]}

机构：

[1] Univ Fed Itajuba, Inst Matemat & Computacao, BR-37500903 Itajuba, MG, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 466卷 / 02期

关键词：

Stability; Symmetric solutions; Mixed boundary conditions; Dirichlet boundary conditions; RIEMANNIAN-MANIFOLDS; STABLE EQUILIBRIA; PARABOLIC EQUATION; VARIABLE DIFFUSION; PATTERNS; REVOLUTION; EXISTENCE; SURFACES; SYSTEMS;

D O I：

10.1016/j.jmaa.2018.06.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we consider a one-dimensional reaction-diffusion problem with mixed boundary conditions. We provide conditions for the existence or nonexistence of stable nonconstant solutions whose derivative vanishes at some point. As an application, we obtain similar results for problems with Dirichlet boundary conditions posed in some symmetric domains: an n-dimensional ball, surfaces of revolution, and model manifolds. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1190 / 1210

页数：21

共 50 条

[41] SOME REMARKS ON A MOVING BOUNDARY-PROBLEM IN A FLUID-FLUID REACTION-DIFFUSION SYSTEM
VILLA, LT
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 142 (02) : 431 - 440
[42] Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition
de Pablo, A
Quirós, F
Rossi, JD
IMA JOURNAL OF APPLIED MATHEMATICS, 2002, 67 (01) : 69 - 98
[43] THE STABILITY OF SOLUTIONS IN AN INITIAL-BOUNDARY REACTION-DIFFUSION SYSTEM
TUMA, E
BLAZQUEZ, CM
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (03) : 441 - 448
[44] Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
Erban, Radek
Chapman, S. Jonathan
PHYSICAL BIOLOGY, 2007, 4 (01) : 16 - 28
[45] Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions
Pao, CV
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 136 (1-2) : 227 - 243
[46] EPIDEMIC REACTION-DIFFUSION SYSTEMS WITH TWO TYPES OF BOUNDARY CONDITIONS
Li, Kehua
Li, Jiemei
Wang, Wei
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[47] Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions
Kucera, Milan
Vaeth, Martin
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (04) : 2951 - 2982
[48] On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions
Arrieta, Jose M.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (01) : 151 - 160
[49] DYNAMICS OF REACTION-DIFFUSION EQUATIONS WITH NONLOCAL BOUNDARY-CONDITIONS
PAO, CV
QUARTERLY OF APPLIED MATHEMATICS, 1995, 53 (01) : 173 - 186
[50] On the existence of patterns in reaction-diffusion problems with Dirichlet boundary conditions
Sonego, Maicon
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2024, (30)

← 1 2 3 4 5 →