Volume effects in the Keller–Segel model: energy estimates preventing blow-up

✍ Scribed by Vincent Calvez; José A. Carrillo

• Book ID: 104044757
• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 206 KB
• Volume: 86
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2006.04.002

✦ Synopsis

We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions.