On a nonlocal moving frame approximation of traveling waves
Arrieta JM, Lopez-Fernandez M, Zuazua E (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Book Volume: 349
Pages Range: 753-758
Journal Issue: 13-14
DOI: 10.1016/j.crma.2011.07.001
Abstract
The profiles of traveling wave solutions of a 1-d reaction-diffusion parabolic equation are transformed into equilibria of a nonlocal equation, by means of an appropriate nonlocal change of variables. In this new formulation both the profile and the propagation speed of the traveling waves emerge as asymptotic limits of solutions of a nonlocal reaction-diffusion problem when time goes to infinity. In this Note we make these results rigorous analyzing the well-posedness and the stability properties of the corresponding nonlocal Cauchy problem. We also analyze its restriction to a finite interval with consistent boundary conditions. For large enough intervals we show that there is an asymptotically stable equilibrium which approximates the profile of the traveling wave in R. This leads to efficient numerical algorithms for computing the traveling wave profile and speed of propagation. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Authors with CRIS profile
Involved external institutions
Universidad Complutense de Madrid (UCM)
Spain (ES)
University of Zurich / Universität Zürich (UZH)
Switzerland (CH)
Ikerbasque (Basque Foundation for Science)
Spain (ES)
Spain (ES)
University of Zurich / Universität Zürich (UZH)
Switzerland (CH)
Ikerbasque (Basque Foundation for Science)
Spain (ES)
How to cite
APA:
Arrieta, J.M., Lopez-Fernandez, M., & Zuazua, E. (2011). On a nonlocal moving frame approximation of traveling waves. Comptes Rendus Mathematique, 349(13-14), 753-758. https://dx.doi.org/10.1016/j.crma.2011.07.001
MLA:
Arrieta, Jose M., Maria Lopez-Fernandez, and Enrique Zuazua. "On a nonlocal moving frame approximation of traveling waves." Comptes Rendus Mathematique 349.13-14 (2011): 753-758.
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