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
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. https://doi.org/10.57262/ade/1355854329
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