Gradient estimates for the Fisher–KPP equation on Riemannian manifolds

被引：0
作者：
Xin Geng
Songbo Hou
机构：
[1] China Agricultural University,Department of Applied Mathematics, College of Science
来源：
Boundary Value Problems | / 2018卷
关键词：
Fisher–KPP equation; Gradient estimate; Harnack inequality; 58J35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider positive solutions to the Fisher–KPP equation on complete Riemannian manifolds. We derive the gradient estimate. Using the estimate, we get the classic Harnack inequality which extends the recent result of Cao, Liu, Pendleton, and Ward (Pac. J. Math. 290(2):273–300, 2017).
引用
收藏
相关论文
共 35 条
[1]  
Cao X.(2017)Differential Harnack estimates for Fisher’s equation Pac. J. Math. 290 273-300
[2]  
Liu B.(1937)The wave of advance of advantageous genes Annu. Eugen. 7 355-369
[3]  
Pendleton I.(1937)Ètude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique Bull. Univ. Mosc. Sér. Int. A 1 1-25
[4]  
Ward A.(2001)Travelling fronts and entire solutions of the Fisher–KPP equation in Arch. Ration. Mech. Anal. 157 91-163
[5]  
Fisher R.A.(2009)Bistable traveling waves around an obstacle Commun. Pure Appl. Math. 62 729-788
[6]  
Kolmogorov A.N.(2007)Asymptotic speeds of spread and traveling waves for monotone semiflows with applications Commun. Pure Appl. Math. 60 1-40
[7]  
Petrovsky I.G.(2008)Differential Harnack estimates for backward heat equations with potentials under the Ricci flow J. Funct. Anal. 255 1024-1038
[8]  
Piskunov N.S.(2009)Differential Harnack estimates for time-dependent heat equations with potentials Geom. Funct. Anal. 19 989-1000
[9]  
Hamel F.(1986)On the parabolic kernel of the Schrödinger operator Acta Math. 156 153-201
[10]  
Nadirashvili N.(1975)Harmonic functions on complete Riemannian manifolds Commun. Pure Appl. Math. 28 201-228
1234