| Abstract: |
| This talk deals with a chemotaxis system with nonlinear diffusion. Colli--Fukao (2015) proved existence of solutions to a Cahn--Hilliard system as an approximation of a nonlinear diffusion equation by applying an abstract theory by Colli--Visintin (1990) for a doubly nonlinear evolution inclusion with some bounded monotone operator and some proper lower semicontinuous convex function. Moreover, Colli--Fukao (2016) established existence of solutions to the nonlinear diffusion equation by passing to the limit in the Cahn--Hilliard equation. However, Cahn--Hilliard approaches to chemotaxis systems with nonlinear diffusions seem not to be studied yet. This talk will try to derive existence of solutions to a chemotaxis system with nonlinear diffusion by passing to the limit in a Cahn--Hilliard type chemotaxis system. |
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