A continuous dependence result for a nonstandard system of phase field equations

TL;DR

This paper establishes a continuous dependence property for a nonstandard phase field system, extending previous results by allowing a variable mobility coefficient depending on the chemical potential.

Contribution

It generalizes the uniqueness result to cases with a non-constant mobility coefficient, enhancing understanding of the system's stability.

Findings

Proved continuous dependence for the system with variable mobility

Extended uniqueness results to more general mobility functions

Provided a rigorous mathematical framework for the limit system

Abstract

The present note deals with a nonstandard systems of differential equations describing a two-species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, an existence result has been proved for the limit system in a very general framework. On the contrary, uniqueness was shown by assuming a constant mobility coefficient. Here, we generalize this result and prove a continuous dependence property in the case that the mobility coefficient suitably depends on the chemical potential.