2016/09/16 by Judith Berendsen, Martin Burger, Berendsen, Judith +3
Materials Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Solidification and crystal growth phenomena #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1609.05024
openalex publication_date 2016/09/16 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
The aim of this paper is to study a PDE model for two diffusing species\ninteracting by local size exclusion and global attraction. This leads to a\nnonlinear degenerate cross-diffusion system, for which we provide a global\nexistence result. The analysis is motivated by the formulation of the system as\na formal gradient flow for an appropriate energy functional consisting of\nentropic terms as well as quadratic nonlocal terms. Key ingredients are entropy\ndissipation methods as well as the recently developed boundedness by entropy\nprinciple. Moreover, we investigate phase separation effects inherent in the\ncross-diffusion model by an analytical and numerical study of minimizers of the\nenergy functional and their asymptotics to a previously studied case as the\ndiffusivity tends to zero. Finally we briefly discuss coarsening dynamics in\nthe system, which can be observed in numerical results and is motivated by\nrewriting the PDEs as a system of nonlocal Cahn-Hilliard equations.\n