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math.AP2024
Nonlocal approximation of an anisotropic cross-diffusion system
Tomasz DÄbiec, Markus Schmidtchen
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems.…
math.AP2024
From Finite to Continuous Phenotypes in (Visco-)Elastic Tissue Growth Models
Tomasz DÄbiec, Mainak Mandal, Markus Schmidtchen
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model…
math.AP2024
Uniform regularity estimates for nonlinear diffusion-advection equations in the hard-congestion limit
Noemi David, Filippo Santambrogio, Markus Schmidtchen
We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drif…