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Abstract and Applied Analysis
Volume 2, Issue 1-2, Pages 47-66
http://dx.doi.org/10.1155/S1085337597000262

Global attractors for two-phase stefan problems in one-dimensional space

Department of Mathematics, Faculty of Education, Gifu University, Gifu 501-11, Japan

Received 20 May 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper 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 𝒜 of autonomous Stefan problem. The main purpose in the present paper is to prove that the set 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.