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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Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123027

Mathematical Reviews number (MathSciNet)
MR1859609

Zentralblatt MATH identifier
1161.35318

Subjects
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.)

Citation

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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