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A system of phase-field equations with strong-coupling through state andgradient dependent non-diagonal mobility matrices is studied. Existence of weaksolutions is established by the Galerkin approximation and a-priori estimatesin strong norms. Relative energy estimates are used to derive a generalnonlinear stability estimate. As a consequence, a weak-strong uniquenessprinciple is obtained and stability with respect to model parameters isinvestigated.

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