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

Authors: A. Brunk, H. Egger, T.D. Oyedeji, Y. Yang, B.-X. Xu

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.