Differential and Integral Equations

Blow-up phenomenon and global solution to a coupled parabolic-elliptic system of chemotaxis

A. Boy-Dalverny and M. Madaune-Tort

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We study a model proposed by E.F. Keller and L.A. Segel in two dimensions. Under some assumptions on the initial datum we prove the global existence and uniqueness of the solution and for other initial values we show that there exists a radial symmetric solution exploding in finite time.

Article information

Differential Integral Equations, Volume 14, Number 11 (2001), 1333-1350.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35K50 35K55: Nonlinear parabolic equations 35K60: Nonlinear initial value problems for linear parabolic equations 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92C17: Cell movement (chemotaxis, etc.)


Boy-Dalverny, A.; Madaune-Tort, M. Blow-up phenomenon and global solution to a coupled parabolic-elliptic system of chemotaxis. Differential Integral Equations 14 (2001), no. 11, 1333--1350. https://projecteuclid.org/euclid.die/1356123027

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