Advances in Differential Equations

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

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

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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

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

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92C15: Developmental biology, pattern formation 92C17: Cell movement (chemotaxis, etc.) 92D15: Problems related to evolution


Harada, Go; Nagai, Toshitaka; Senba, Takasi; Suzuki, Takashi. Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis. Adv. Differential Equations 6 (2001), no. 10, 1255--1280.

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