# Global existence for a phase separation system deduced from the entropy balance

## TL;DR

This paper proves the global existence of solutions for a complex thermomechanical phase separation model based on entropy balance, encompassing both viscous and non-viscous cases with singular potentials.

## Contribution

It introduces a novel analysis of a nonlinear, entropy-based phase separation system with singular potentials, establishing global existence results.

## Key findings

- Global solutions exist for the model
- The analysis covers both viscous and non-viscous cases
- Use of Yosida regularizations and time discretization techniques

## Abstract

This paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces. The related system is highly nonlinear and admits singular potentials in the phase equation. Both the viscous and the non-viscous cases are considered in the Cahn--Hilliard relations characterizing the phase dynamics. The entropy balance is written in terms of the absolute temperature and of its logarithm, appearing under time derivative. The initial and boundary value problem is considered for the system of partial differential equations. The existence of a global solution is proved via some approximations involving Yosida regularizations and a suitable time discretization.