Global attractors for two-phase Stefan problems in one-dimensional space
type: Item
instance of: scholarly article
title: Global attractors for two-phase Stefan problems in one-dimensional space
zbMATH Open document ID: 0939.35032
DOI: 10.1155/S1085337597000262
published in: Abstract and Applied Analysis
publication date: 2000-07-12T00:00:00Z
full work available at URL: https://eudml.org/doc/48449
full work available at URL: issue-1-2.html
review text: Summary: We consider one-dimensional two-phase Stefan problems for a class of parabolic equations with nonlinear heat source terms and with nonlinear flux conditions on the fixed boundary. Here, both time-dependent and time-independent source terms and boundary conditions are treated. We investigate the large time behavior of solutions to our problems by using the theory for dynamical systems. First, we show the existence of a global attractor \({\mathcal A}\) of an autonomous Stefan problem. The main purpose in the present paper is to prove that the set \({\mathcal A}\) attracts all solutions of non-autonomous Stefan problems as time tends to infinity under the assumption that time-dependent data converge to time-independent ones as time goes to infinity.
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 1370670
zbMATH Keywords: nonlinear heat source terms
zbMATH Keywords: nonlinear flux conditions on the fixed boundary
author: Toyohiko Aiki
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1370670