Pure cross-diffusion models: Implications for traveling wave solutions
Populations and Evolution
2008-07-11 v1 Pattern Formation and Solitons
Quantitative Methods
Abstract
An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different types of wave solutions are formulated. In particular, it is shown that family of wave trains is a generic phenomenon in pure cross-diffusion systems. The results can be used for construction and analysis of different mathematical models describing systems with directional movement.
Cite
@article{arxiv.0807.1655,
title = {Pure cross-diffusion models: Implications for traveling wave solutions},
author = {Faina S. Berezovskaya and Georgy P. Karev and Artem S. Novozhilov},
journal= {arXiv preprint arXiv:0807.1655},
year = {2008}
}
Comments
11 pages, 5 figues