arXiv subjects

M. Wechselberger

Publications and source records attributed to M. Wechselberger.

2 recordsLinked to original sources

arXiv2020

(In)Stability of Travelling Waves in a Model of Haptotaxis

We examine the spectral stability of travelling waves of the haptotaxis model studied in Harley et al (2014a). In the process we apply Liénard coordinates to the linearised stability problem and use a Riccati-transform/Grassmanian spectral shooting method á la Harley et al (2015), Ledoux et al (2009) and Ledoux et al (2010) in order to numerically compute the Evans function and point spectrum of a linearised operator associated with a travelling wave. We numerically show the instability of non-monotone waves (type IV) and the stability of the monotone ones (types I-III) to perturbations in an appropriately weighted space.

math.DS↗

arXiv2015

Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed $c \geq 2 \sqrtδ$ in the F-KPP equation.

math.SP↗