Vol. 290, No. 2, 2017

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ISSN: 0030-8730
Differential Harnack estimates for Fisher's equation

Xiaodong Cao, Bowei Liu, Ian Pendleton and Abigail Ward

Vol. 290 (2017), No. 2, 273–300
Abstract

We derive several differential Harnack estimates (also known as Li–Yau–Hamilton-type estimates) for positive solutions of Fisher’s equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions and to construct classical Harnack inequalities.

Keywords
differential Harnack, classical Harnack, Fisher's equation, Fisher–KPP, traveling wave
Mathematical Subject Classification 2010
Primary: 58J35, 35K59
Milestones
Received: 26 October 2015
Revised: 30 August 2016
Accepted: 28 September 2016
Published: 25 July 2017
Authors
Xiaodong Cao
Department of Mathematics
Cornell University
Ithaca, NY 14853
United States
Bowei Liu
Department of Mathematics
Stanford University
Stanford, CA 94305
United States
Ian Pendleton
Department of Mathematics
Cornell University
Ithaca, NY 14853
United States
Abigail Ward
Department of Mathematics
The University of Chicago
Chicago, IL 60637
United States