Global and exponential attractors for the Penrose-Fife system

TL;DR

This paper proves the existence of global and exponential attractors for the Penrose-Fife system, a phase transition model with complex energy behavior, demonstrating dissipativity despite singular and degenerate energy conditions.

Contribution

It establishes the existence of attractors for the Penrose-Fife system with singular and degenerate energy, advancing understanding of its long-term dynamics.

Findings

Existence of global attractors proved.

Existence of exponential attractors proved.

Dissipativity established despite energy singularities.

Abstract

The Penrose-Fife system for phase transitions is addressed. Dirichlet boundary conditions for the temperature are assumed. Existence of global and exponential attractors is proved. Differently from preceding contributions, here the energy balance equation is both singular at 0 and degenerate at infinity. For this reason, the dissipativity of the associated dynamical process is not trivial and has to be proved rather carefully.