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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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140394

Mathematical Reviews number (MathSciNet)
MR1850389

Zentralblatt MATH identifier
1009.35043

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ade/1357140394.


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