On existence, uniqueness and stability of solutions to Cahn–Hilliard/Allen–Cahn systems with cross-kinetic coupling
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Abstract
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.
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Nonlinear analysis / Real world applications, 77, Elsevier Science, Amsterdam [u.a.], 2024, https://doi.org/10.1016/j.nonrwa.2023.104051