## Abstract and Applied Analysis

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

T. Aiki

#### 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 $\mathcal{A}$ of 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2, Number 1-2 (1997), 47-66.

Dates
First available in Project Euclid: 7 April 2003

https://projecteuclid.org/euclid.aaa/1049737242

Digital Object Identifier
doi:10.1155/S1085337597000262

Mathematical Reviews number (MathSciNet)
MR1604232

Zentralblatt MATH identifier
0939.35032

Subjects
Primary: 35K22
Secondary: 65R35 35B35: Stability

#### Citation

Aiki, T. Global attractors for two-phase stefan problems in one-dimensional space. Abstr. Appl. Anal. 2 (1997), no. 1-2, 47--66. doi:10.1155/S1085337597000262. https://projecteuclid.org/euclid.aaa/1049737242