N-barrier maximum principle for degenerate elliptic systems and its application
Analysis of PDEs
2016-09-06 v1
Abstract
In this paper, we prove the N-barrier maximum principle, which extends the result in [5] from linear diffusion equations to nonlinear diffusion equations, for a wide class of degenerate elliptic systems of porous medium type. The N-barrier maximum principle provides a priori upper and lower bounds of the solutions to the above-mentioned degenerate nonlinear diffusion equations including the Shigesada-Kawasaki-Teramoto model as a special case. As an application of the N-barrier maximum principle to a coexistence problem in ecology, we show the nonexistence of waves in a three-species degenerate elliptic systems.
Cite
@article{arxiv.1609.00979,
title = {N-barrier maximum principle for degenerate elliptic systems and its application},
author = {Li-Chang Hung and Hsiao-Feng Liu and Chiun-Chuan Chen},
journal= {arXiv preprint arXiv:1609.00979},
year = {2016}
}