On conserved Penrose-Fife type models

TL;DR

This paper analyzes conserved Penrose-Fife models, establishing maximal regularity, global existence under temperature bounds, and convergence to steady states using advanced mathematical tools.

Contribution

It provides the first comprehensive analysis of quasilinear parabolic systems of this type, including regularity, existence, and long-term behavior results.

Findings

Maximal Lp-regularity for the system with inhomogeneous boundary data

Global existence of solutions under temperature bounds

Solutions converge to steady states over time

Abstract

In this paper we investigate quasilinear parabolic systems of conserved Penrose-Fife type. We show maximal $L_p$ - regularity for this problem with inhomogeneous boundary data. Furthermore we prove global existence of a solution, provided that the absolute temperature is bounded from below and above. Moreover, we apply the Lojasiewicz-Simon inequality to establish the convergence of solutions to a steady state as time tends to infinity.