Layers in the presence of conservation laws
type: Item
instance of: scholarly article
title: Layers in the presence of conservation laws
zbMATH Open document ID: 1260.37051
author: Alin Pogan
author: Arnd Scheel
published in: Journal of Dynamics and Differential Equations
publication date: 2012-06-26T00:00:00Z
review text: In this paper, the authors consider systems where a scalar conservation law is coupled to a scalar reaction-diffusion equation. They start by indicating how to construct a layer solution and they show how it can be found in the system considered. The main result of this paper concerns the characterization of the stability of layers in these systems. Obtaining a non-linear second-order pendulum equation which can have homoclinic, periodic or heteroclinic solutions. The authors concentrate on the last type. In order to investigate the eigenvalue problem, it is shown that this problem near \(\lambda=0\) can be recasted as a bifurcation problem. The authors use then Lyapunov-Shmidt reduction to approach it. In the last two sections, the main theorems of this paper are proved.
Mathematics Subject Classification ID: 37L15
zbMATH DE Number: 6050503
zbMATH Keywords: Heteroclinic solutions
zbMATH Keywords: conservation law
zbMATH Keywords: Stability
zbMATH Keywords: Lyapunov-Schmidt reduction
MaRDI profile type: Publication
full work available at URL: s10884-012-9248-3
OpenAlex ID: W2021035479
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DOI: 10.1007/S10884-012-9248-3
description: scientific article; zbMATH DE number 6050503