Global weak solutions to a fractional Cahn-Hilliard cross-diffusion system in lymphangiogenesis

• DOI: 10.48550/arxiv.2408.05972
• Publication Date: 2024-08-12
• Authors: Ansgar Jüngel; Yue Li
• Keywords: Lymphangiogenesis

A spectral-fractional Cahn-Hilliard cross-diffusion system, which describes the pre-patterning of lymphatic vessel morphology in collagen gels, is studied. The model consists two higher-order quasilinear parabolic equations and evolution fiber phase volume fraction solute concentration. free energy nonconvex Flory-Huggins a fractional gradient energy, modeling nonlocal long-range correlations. existence global weak solutions to this system bounded domain with no-flux boundary conditions shown. proof based on three-level approximation scheme, calculus, priori estimates coming from inequality.