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January/February 2011 Local well posedness and instability of travelling waves in a chemotaxis model
Martin Meyries
Adv. Differential Equations 16(1/2): 31-60 (January/February 2011).

Abstract

We consider the Keller-Segel model for chemotaxis with a nonlinear diffusion coefficent and a singular sensitivity function. We show the existence of travelling waves for wave speeds above a critical value, and establish local well posedness in exponentially weighted spaces in a neighbourhood of a wave. A part of the essential spectrum of the linearization, which has unbounded coefficients on one half-axis, is determined. Generalizing the principle of linearized instability without spectral gap to fully nonlinear parabolic problems, we obtain nonlinear instability of the waves in certain cases.

Citation

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Martin Meyries. "Local well posedness and instability of travelling waves in a chemotaxis model." Adv. Differential Equations 16 (1/2) 31 - 60, January/February 2011.

Information

Published: January/February 2011
First available in Project Euclid: 18 December 2012

zbMATH: 1228.35056
MathSciNet: MR2766893

Subjects:
Primary: 35B40, 35G25, 35K55, 47D06, 47E05, 92B05

Rights: Copyright © 2011 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.16 • No. 1/2 • January/February 2011
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