Approximating travelling waves by equilibria of non-local equations

Arrieta JM, Lopez-Fernandez M, Zuazua E (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Asymptotic Analysis IOS Press

Book Volume: 78

Pages Range: 145-186

Journal Issue: 3

DOI: 10.3233/ASY-2011-1088

Abstract

We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously the travelling wave profile and its propagation speed avoiding moving meshes, as we illustrate with several numerical examples. We analyze the relation of the new equation with the original one in the entire real line. We also analyze the behavior of the non-local problem in a bounded interval with appropriate boundary conditions. We show that it has a unique stationary solution which approaches the traveling wave as the interval gets larger and larger and that is asymptotically stable for large enough intervals.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Universidad Complutense de Madrid (UCM) ES Spain (ES) University of Zurich / Universität Zürich (UZH) CH Switzerland (CH) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Arrieta, J.M., Lopez-Fernandez, M., & Zuazua, E. (2012). Approximating travelling waves by equilibria of non-local equations. Asymptotic Analysis, 78(3), 145-186. https://doi.org/10.3233/ASY-2011-1088

MLA:

Arrieta, Jose M., Maria Lopez-Fernandez, and Enrique Zuazua. "Approximating travelling waves by equilibria of non-local equations." Asymptotic Analysis 78.3 (2012): 145-186.

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