English

Harnack Estimate for the Endangered Species Equation

Analysis of PDEs 2015-06-30 v1

Abstract

We prove a differential Harnack inequality for the Endangered Species Equation, a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blowup in finite time. We also use this inequality to partially answer a question of Hamilton, 2011.

Keywords

Cite

@article{arxiv.1406.7033,
  title  = {Harnack Estimate for the Endangered Species Equation},
  author = {Xiaodong Cao and Mark Cerenzia and Demetre Kazaras},
  journal= {arXiv preprint arXiv:1406.7033},
  year   = {2015}
}

Comments

To appear in Proceedings of the American Mathematical Society (2014)

R2 v1 2026-06-22T04:48:36.815Z