Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion Systems
Analysis of PDEs
2019-06-11 v1
Abstract
We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. No boundedness assumption on these solutions is supposed here as known techniques for scalar equations such as maximum/comparison principles are generally unavailable for systems. Furthermore, for planar domains we show that unbounded weak solutions satisfying mild integrability conditions are in fact smooth.
Cite
@article{arxiv.1906.03456,
title = {Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion Systems},
author = {Dung Le},
journal= {arXiv preprint arXiv:1906.03456},
year = {2019}
}