Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations
Abstract
We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical results on the existence, uniqueness (up to translations) and stability of a traveling wave solution connecting two stable homogeneous steady states. Moreover, we review numerical methods for the case of reaction-diffusion equations with fractional Laplacian and discuss possible extensions to our reaction-diffusion equations with Riesz-Feller operators. In particular, we present a direct method using integral operator discretization in combination with projection boundary conditions to visualize our analytical results about traveling waves.
Keywords
Cite
@article{arxiv.1405.5779,
title = {Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations},
author = {Franz Achleitner and Christian Kuehn},
journal= {arXiv preprint arXiv:1405.5779},
year = {2017}
}
Comments
22 pages; 4 figures; the paper provides an overview and the numerical simulation component / visualization of the analytical results in arXiv:1312.6304