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arXiv · 2401.05180

Existence of global weak solutions to a Cahn-Hilliard cross-diffusion system in lymphangiogenesis

Ansgar Jüngel·Yue Li
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Abstract

The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic fourth-order partial differential equations and describes the evolution of the fiber phase volume fraction and the solute concentration, modeling the pre-patterning of lymphatic vessel morphology. The fiber phase fraction satisfies the segregation property if this holds initially. The existence proof is based on a three-level approximation scheme and a priori estimates coming from the energy and entropy inequalities. While the free energy is nonincreasing in time, the entropy is only bounded because of the cross-diffusion coupling.

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Ansgar Jüngel, Yue Li. 2024-01-10. Existence of global weak solutions to a Cahn-Hilliard cross-diffusion system in lymphangiogenesis. https://arxiv.org/abs/2401.05180

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