On existence, uniqueness and stability of solutions to Cahn-Hilliard/Allen-Cahn systems with cross-kinetic coupling

TL;DR

This paper investigates the mathematical properties of coupled Cahn-Hilliard/Allen-Cahn systems with complex mobility matrices, establishing existence, stability, and uniqueness of solutions through advanced analytical techniques.

Contribution

It introduces new existence and stability results for strongly coupled phase-field systems with non-diagonal mobility matrices, extending previous theoretical frameworks.

Findings

Existence of weak solutions via Galerkin approximation.

Derivation of nonlinear stability estimates.

Weak-strong uniqueness principle established.

Abstract

A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by the Galerkin approximation and a-priori estimates in strong norms. Relative energy estimates are used to derive a general nonlinear stability estimate. As a consequence, a weak-strong uniqueness principle is obtained and stability with respect to model parameters is investigated.