Harnack estimate for the Endangered Species Equation

Cao, Xiaodong; Cerenzia, Mark; Kazaras, Demetre

doi:10.1090/S0002-9939-2015-12576-2

Harnack estimate for the Endangered Species Equation
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by Xiaodong Cao, Mark Cerenzia and Demetre Kazaras PDF

Proc. Amer. Math. Soc. 143 (2015), 4537-4545 Request permission

Abstract:

We prove a differential Harnack inequality for the Endangered Species Equation, which is 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 blow up in finite time.

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