Advances in Differential Equations

A fast blowup solution to an elliptic-parabolic system related to chemotaxis

Takasi Senba

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We consider radial blowup solutions to an elliptic-parabolic system in $N$-dimensional Euclidean space. The system is introduced to describe several phenomena, for example, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters. In the case where $N \geq 3$, we can find positive and radial backward self-similar solutions which blow up in finite time. In the present paper, in the case where $N \geq 11$, we show the existence of a radial blowup solution whose blowup speed is faster than the one of backward self-similar solutions, by using so-called asymptotic matched expansion techniques.

Article information

Adv. Differential Equations, Volume 11, Number 9 (2006), 981-1030.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92C17: Cell movement (chemotaxis, etc.)


Senba, Takasi. A fast blowup solution to an elliptic-parabolic system related to chemotaxis. Adv. Differential Equations 11 (2006), no. 9, 981--1030.

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