Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis

Abstract

We study a system of parabolic equations introduced by E.F. Keller and L.A. Segel to describe the chemotactic feature of slime molds. Concentration toward the boundary is shown for the blowup solution with the total mass less than $8\pi$. For this purpose, a variant of the concentration lemma of Chang and Yang's type, and also a parabolic version of an inequality due to Brezis and Merle, are provided.

Article information

Source
Adv. Differential Equations, Volume 6, Number 10 (2001), 1255-1280.

Dates
First available in Project Euclid: 2 January 2013