Advances in Differential Equations

Local well posedness and instability of travelling waves in a chemotaxis model

Martin Meyries

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Adv. Differential Equations, Volume 16, Number 1/2 (2011), 31-60.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions 35G25: Initial value problems for nonlinear higher-order equations 35K55: Nonlinear parabolic equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) 92B05: General biology and biomathematics


Meyries, Martin. Local well posedness and instability of travelling waves in a chemotaxis model. Adv. Differential Equations 16 (2011), no. 1/2, 31--60.

Export citation