Long time convergence for a class of variational phase field models

TL;DR

This paper investigates the long-term behavior of a class of phase field models for phase transitions, establishing existence, uniqueness, regularity, and convergence properties of solutions over time.

Contribution

It extends classical phase field models by analyzing their long-time convergence and regularity, providing new theoretical insights into their dynamics.

Findings

Existence and uniqueness of solutions proved.

Solutions exhibit regularizing effects over time.

Trajectory converges as time approaches infinity.

Abstract

In this paper we analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife models. Existence and uniqueness of the solution to the related initial boundary value problem are shown. Further regularity of the solution is deduced by exploiting the so-called regularizing effect. Then, the large time behavior of such a solution is studied and several convergence properties of the trajectory as time tends to infinity are discussed.