Abstract:This talk addresses an initial-boundary problem for a quasilinear chemotaxis system with indirect attractant production, as arising in the modeling of effects due to phenotypical heterogeneity in microbial populations. Under the assumption that the rates $D$ and $S$ of diffusion and cross-diffusion are suitably regular functions of the population density, essentially exhibiting asymptotically algebraic behavior at large densities. A critical line in low-dimensional cases and two critical lines in higher-dimensional cases concerning the exponents of $D$ and $S$ for the occurrence of blow-up were found. This is a recent joint work with Prof. Michael Winkler (Paderborn).
腾讯会议：107-930-142
