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

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.