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arXiv · 1406.7033

Harnack Estimate for the Endangered Species Equation

Xiaodong Cao·Mark Cerenzia·Demetre Kazaras
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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.

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Xiaodong Cao, Mark Cerenzia, Demetre Kazaras. 2014-06-26. Harnack Estimate for the Endangered Species Equation. https://doi.org/10.1090/s0002-9939-2015-12576-2#sthash.8pd3n3rm.dpuf

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