Existence and uniqueness of positive stationary solution to a reaction diffusion system from biology
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive stationary solution to a reaction diffusion system from biology
zbMATH Open document ID: 0827.35047
author: Mingxin Wang
published in: Chinese Science Bulletin
publication date: 1995-11-29T00:00:00Z
review text: The system \[ - \Delta u = f(u) - v,\;- \Delta v = \delta u - \gamma v,\;x \in \Omega,\;u = v,x \in \partial \Omega \tag{1} \] where \(\Omega \subset \mathbb{R}^n\) is a bounded open domain, \(\partial \Omega \in C^\alpha\), \(\delta, \gamma > 0\), is interpreted as stationary model for relative concentrations of substances known as morphogens. The author proves, under some conditions concerning the eigenvalues of \(-\Delta\), that the system (1) has a nontrivial and nonnegative solution and that this solution is unique.
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 722356
zbMATH Keywords: positive stationary solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 722356