Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in \(N\)-dimensional domains
type: Item
instance of: scholarly article
title: Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in \(N\)-dimensional domains
zbMATH Open document ID: 1019.35008
DOI: 10.1016/S0022-0396(02)00147-X
author: Arnaldo Simal do Nascimento
published in: Journal of Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The author proves existence and establishes the asymptotic behavior, as \(\varepsilon\rightarrow 0\), of stable stationary solutions to the equation \(u_{t}=\varepsilon\bigtriangledown\cdot[d(x)\bigtriangledown u]+ (1-u^{2})[u-a(x)]\), for \((t,x)\in \mathbb{R}^{+}\times\Omega\), where \(\Omega\subset\mathbb{R}^{N},\;N\geq 2\), with Neumann boundary condition. The function \(a(x)\in C^{0,v}(\Omega)\) satisfies \(-1<a(x)<1\) and varies on some hypersurfaces.
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 1915651
zbMATH Keywords: stable stationary solutions
zbMATH Keywords: Neumann boundary condition
reviewed by: Jiaqi Mo
MaRDI profile type: Publication
cites work: Stable transition layers in a semilinear boundary value problem
cites work: On the Singular Limit for a Cass of Problems Modelling Phase Transitions
cites work: Q3140494
cites work: Uniform convergence of a singular perturbation problem
cites work: Elliptic Problems Involving Phase Boundaries Satisfying a Curvature Condition
cites work: INTERIOR TRANSITION LAYERS FOR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH A SMALL PARAMETER
cites work: Stable Equilibria in a Scalar Parabolic Equation with Variable Diffusion
cites work: Multiple internal layer solutions generated by spatially oscillatory perturbations
cites work: Existence and stability of transition layers
cites work: Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
cites work: Stability in a semilinear boundary value problem via invariant conefields
cites work: Q4379839
cites work: Stable stationary solutions induced by spatial inhomogeneity via ?-convergence
cites work: On the role of diffusivity in some stable equilibria of a diffusion equation
cites work: Inner transition layers in an elliptic boundary value problem: a necessary condition
cites work: On the convergence of stable phase transitions
cites work: Layers With Nonsmooth Interface in a Semilinear Elliptic Problem
cites work: Q3791584
cites work: Change of variables for absolutely continuous functions
description: scientific article; zbMATH DE number 1915651