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arXiv · 2211.07153

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

Aaron Brunk·Herbert Egger·Timileyin David Oyedeji·Yangyiwei Yang·Bai-Xiang Xu
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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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Aaron Brunk, Herbert Egger, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu. 2022-11-14. On existence, uniqueness and stability of solutions to Cahn-Hilliard/Allen-Cahn systems with cross-kinetic coupling. https://arxiv.org/abs/2211.07153

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