English

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.

Keywords

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}
}
R2 v1 2026-06-22T15:39:38.823Z