A. Aldurayhim, V. N. Biktashev,
Submitted to SIADS 2020/04/16. Submitted to CSFX 2020/04/29. Accepted 2020/09/15. Published: 2020/09/25 as CSFX 5:100049, 2020
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy reaction-cross-diffusion model with exact solutions in the form of propagating fronts. We propose a minimal model of this kind which involves two species linked by cross-diffusion, one of which governed by a linear equation and the other having a polynomial kinetic term. We classify the resulting exact propagating front solutions. Some of them have some features of the Fisher-KPP fronts and some features of the ZFK-Nagumo fronts.
DOI: 10.1016/j.csfx.2020.100049Preprint and/or other related files:
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