Portal de Periódicos da CAPES

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

2001; Volume: 6; Issue: 10 Linguagem: Inglês

10.57262/ade/1357140394

1079-9389

Go Harada, Toshitaka Nagai, Takasi Senba, Takashi Suzuki,

Advanced Mathematical Modeling in Engineering

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.