Harnack Estimate for the Endangered Species Equation
arXiv:1406.7033 · doi:10.1090/S0002-9939-2015-12576-2#sthash.8PD3n3rm.dpuf
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.
To appear in Proceedings of the American Mathematical Society (2014)