On a model of a population with variable motility
Analysis of PDEs
2016-03-07 v2
Abstract
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton-Jacobi equation.
Cite
@article{arxiv.1409.4679,
title = {On a model of a population with variable motility},
author = {Olga Turanova},
journal= {arXiv preprint arXiv:1409.4679},
year = {2016}
}
Comments
36 pages; improved exposition from previous version