Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model

TL;DR

This paper proves that solutions to the Penrose-Fife phase transition model become regular over time and are uniformly bounded, under weaker initial conditions than previously required.

Contribution

It improves existing results by establishing uniqueness and asymptotic regularization of solutions with weaker initial data assumptions.

Findings

Solutions are uniquely determined under weak initial conditions.

Weak solutions exhibit asymptotic regularization over time.

Energy solutions are uniformly bounded asymptotically.

Abstract

We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the initial data. Moreover, we prove asymptotic regularization properties of weak solutions.