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Harnack estimate for the Endangered Species Equation


Authors: Xiaodong Cao, Mark Cerenzia and Demetre Kazaras
Journal: Proc. Amer. Math. Soc. 143 (2015), 4537-4545
MSC (2010): Primary 58J35
Published electronically: March 31, 2015
MathSciNet review: 3373951
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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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Additional Information

Xiaodong Cao
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email: cao@math.cornell.edu

Mark Cerenzia
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Address at time of publication: Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544
Email: cerenzia@princeton.edu

Demetre Kazaras
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: demetre@uoregon.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12576-2
Keywords: Differential Harnack inequality, Endangered Species Equation
Received by editor(s): February 10, 2014
Received by editor(s) in revised form: June 19, 2014
Published electronically: March 31, 2015
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society