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.References
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Additional Information
- Xiaodong Cao
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
- MR Author ID: 775164
- 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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4537-4545
- MSC (2010): Primary 58J35
- DOI: https://doi.org/10.1090/S0002-9939-2015-12576-2
- MathSciNet review: 3373951