Well-posedness for chemotaxis dynamics with nonlinear cell diffusion
This article is concerned with the well-posedness of reaction-diffusion chemotaxis systems with a nonlinear diffusion coefficient, depending on the cell density, and a stationary chemo-attractant. Two cases of diffusion coefficients are discussed: the first case assumes a smooth, locally bounded diffusion coefficient. The second case assumes a singularity in the diffusion coefficient for a finite value of the cell density. Conditions for both local and global existence of weak solutions are investigated. Results include small and large data global existence results and, under more restrictive conditions, uniqueness results on all or part of the interval of existence.
scientific article; zbMATH DE number 6156135
scientific article