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Differential Harnack
estimates for Fisher's equation
Xiaodong Cao, Bowei Liu, Ian Pendleton and Abigail Ward |
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Vol. 290 (2017), No. 2, 273–300
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 58J35, 35K59
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Milestones
Received: 26 October 2015
Revised: 30 August 2016
Accepted: 28 September 2016
Published: 25 July 2017
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Authors |
| Xiaodong Cao | |
| Department of Mathematics Cornell University Ithaca, NY 14853 United States |
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| Bowei Liu | |
| Department of Mathematics Stanford University Stanford, CA 94305 United States |
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| Ian Pendleton | |
| Department of Mathematics Cornell University Ithaca, NY 14853 United States |
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| Abigail Ward | |
| Department of Mathematics The University of Chicago Chicago, IL 60637 United States |
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