On the local in time well-posedness of an elliptic-parabolic ferroelectric phase-field model

TL;DR

This paper proves the local in time well-posedness of a complex coupled elliptic-parabolic ferroelectric phase-field model using fixed point and maximal regularity theories, under general and specific conditions.

Contribution

It introduces a rigorous mathematical proof of well-posedness for a modern ferroelectric model, extending prior work with precise geometric and regularity conditions.

Findings

Established local in time existence and uniqueness of solutions.

Provided geometric and regularity conditions for model assumptions.

Applied fixed point theorem and maximal regularity theory effectively.

Abstract

We consider a state-of-the-art ferroelectric phase-field model arising from the engineering area in recent years, which is mathematically formulated as a coupled elliptic-parabolic differential system. We utilize a fixed point theorem based on the maximal parabolic regularity theory to show the local in time well-posedness of the ferroelectric problem. The well-posedness result will firstly be proved under certain general assumptions. We then give precise geometric and regularity conditions which will guarantee the fulfillment of the assumptions.