Local well-posedness and instability of travelling waves in a chemotaxis model
Analysis of PDEs
2012-02-20 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1202.3880,
title = {Local well-posedness and instability of travelling waves in a chemotaxis model},
author = {Martin Meyries},
journal= {arXiv preprint arXiv:1202.3880},
year = {2012}
}
Comments
This preprint version. Published in Advances in Differential Equations 16 (2011) 31-60