Dynamical spike solutions in a nonlocal model of pattern formation
Analysis of PDEs
2017-06-20 v2
Abstract
Coupling a reaction-diffusion equation with ordinary differential equations (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns.
Cite
@article{arxiv.1307.6236,
title = {Dynamical spike solutions in a nonlocal model of pattern formation},
author = {Anna Marciniak-Czochra and Steffen Härting and Grzegorz Karch and Kanako Suzuki},
journal= {arXiv preprint arXiv:1307.6236},
year = {2017}
}
Comments
25 pages, 4 figures