The Keller–Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion

• DOI: 10.1137/050637923
• Publication Date: 2007-02-21T19:52:06Z
• Authors: Martin Burger; Marco Di Francesco; Yasmin Dolak‐Struss
• Keywords: Zero (linguistics); Constant (computer programming)

The aim of this paper is to discuss the effects linear and nonlinear diffusion in large time asymptotic behavior Keller–Segel model chemotaxis with volume filling effect. In case we provide several sufficient conditions for part dominate yield decay zero solutions. We also an explicit rate towards self–similarity. Moreover, prove that no stationary solutions positive mass exist. fully determined by whether diffusivity constant larger or smaller than threshold value $\varepsilon =1$. Below have existence nondecaying their convergence (along subsequences) For >1$ all compactly supported are proved asymptotically zero, unlike classical models diffusion, where depends on initial mass.