On attractors for a sharp interface model of exothermic phase transitions

TL;DR

This paper investigates a free interface model for exothermic phase transitions, demonstrating the existence of a compact attractor and suggesting its finite fractal dimension through numerical evidence.

Contribution

It establishes the existence of a compact connected attractor for solutions of a phase transition model, with insights into its potential fractal properties.

Findings

Solutions are uniformly bounded.

Interface velocity is smooth.

Existence of a compact attractor proven.

Abstract

We study a free interface problem related to combustion of condensed matter and some non-equilibrium exothermal phase transitions. In spite of a variety of non-trivial dynamical scenarios exhibited by the model the solutions are uniformly bounded and the interface velocity is a smooth function. The main result of the paper establishes existence of a compact connected attractor for the classical solutions of the problem. Numerical evidence leads to the conjecture that the fractal dimension of the attractor is finite.