On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity
type: Item
instance of: scholarly article
title: On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity
zbMATH Open document ID: 0806.35134
DOI: 10.1007/BF02790230
author: Gershon Wolansky
published in: Journal d'Analyse Mathématique
publication date: 1994-10-18T00:00:00Z
review text: The elliptic boundary value problem of the form \[ \Delta u = \lambda \exp \bigl( -(u + v) \bigr) \quad \text{in } G, \qquad \int \partial u/ \partial n = M \quad \text{on } \partial G, \] is considered, where \(G \subset \mathbb{R}^ n\) is a bounded domain, \(V \in L^ \infty(G)\), \(M>0\), \(\lambda>0\) and \(u\) satisfies an additional compatible boundary condition. A free energy functional \(F\) is introduced with a constraint and its behaviour is studied. Using the method of Kazdan-Warner, a solution is obtained as a global minimizer of \(F\). Radial symmetry of solutions is also considered.
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 49J05
zbMATH DE Number: 640327
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: radial symmetry
zbMATH Keywords: global minimizer
reviewed by: Stepan Agop Tersian
MaRDI profile type: Publication
cites work: Q3782303
cites work: Q3876353
cites work: Q3923307
cites work: Curvature functions for compact 2-manifolds
cites work: Q3272715
cites work: Q5562267
cites work: Q5653193
cites work: Q3971308
cites work: On steady distributions of self-attracting clusters under friction and fluctuations
description: scientific article; zbMATH DE number 640327