A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation  

作　　者：Derek Booth Jack Burkart Xiaodong Cao Max Hallgren Zachary Munro Jason Snyder Tom Stone 

机构地区：[1]Department of Mathematics,Harvard University,Cambridge,MA 02138,USA [2]Department of Mathematics,Stony Brook University,Stony Brook,NY 11794,USA [3]Department of Mathematics,Cornell University,Ithaca,NY 14853-4201,USA [4]Department of Mathematics and Statistics,McGill University,Montreal,Canada [5]Department of Mathematics,University of California,Los Angeles,Los Angeles,CA90095,USA [6]Department of Mathematics,Brown Univeristy,Providence,RI 02912,USA

出　　处：《Analysis in Theory and Applications》2019年第2期192-204,共13页分析理论与应用（英文刊）

基　　金：supported by NSF through the Research Experience for Undergraduates Program at Cornell University, grant-1156350;supported by Cornell University Summer Program for Undergraduate Research;partially supported by a grant from the Simons Foundation (#280161)

摘　　要：This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on Rn. We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation, including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.

关 键 词：Newell-Whitehead-Segel EQUATION Harnack ESTIMATE Harnack INEQUALITY WAVE solutions. 

分 类 号：O1[理学—数学]