Spreading in a cone for the Fisher-KPP equation

被引：3

作者：

Lou, Bendong ^{[1
]}

Lu, Junfan ^{[2
]}

机构：

[1] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 12期

关键词：

Fisher-KPP equation; Cone; Spreading phenomena; Steady state; Traveling wave solution; FAST DIFFUSION; MODEL;

D O I：

10.1016/j.jde.2019.07.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the spreading phenomena in the Fisher-KPP equation in a high dimensional cone with Dirichlet boundary condition. We show that any solution starting from a nonnegative and compact supported initial data spreads and converges to the unique positive steady state. Moreover, the asymptotic spreading speeds of the front in all directions pointing to the opening are c(0) (which is the minimal speed of the traveling wave solutions of the 1-dimensional Fisher-KPP equation). Surprisingly, they do not depend on the shape of the cone, the propagating directions and the boundary condition. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：7064 / 7084

页数：21

共 50 条

[31] A FREE BOUNDARY PROBLEM FOR THE FISHER-KPP EQUATION WITH A GIVEN MOVING BOUNDARY
Matsuzawa, Hiroshi
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (05) : 1821 - 1852
[32] Dynamics of interfaces in the Fisher-KPP equation for slowly decaying initial data
Ninomiya, Hirokazu
Yanagida, Eiji
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (08) : 4922 - 4947
[33] Doubly nonlocal Fisher-KPP equation: Speeds and uniqueness of traveling waves
Finkelshtein, Dmitri
Kondratiev, Yuri
Tkachov, Pasha
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 475 (01) : 94 - 122
[34] Asymptotic Behavior of Solutions of Free Boundary Problems for Fisher-KPP Equation
Jingjing Cai
Hong Gu
Journal of Dynamics and Differential Equations, 2021, 33 : 913 - 940
[35] Asymptotic behavior of solutions of a degenerate Fisher-KPP equation with free boundaries
Sun, Ningkui
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 24 : 98 - 107
[36] New travelling wave solutions for the Fisher-KPP equation with general exponents
Sánchez-Valdés, A
Hernández-Bermejo, B
APPLIED MATHEMATICS LETTERS, 2005, 18 (11) : 1281 - 1285
[37] Hopf bifurcation of traveling wave solutions of delayed Fisher-KPP equation
Yang, Gaoxiang
APPLIED MATHEMATICS AND COMPUTATION, 2013, 220 : 213 - 220
[38] Asymptotic Behavior of Solutions of Free Boundary Problems for Fisher-KPP Equation
Cai, Jingjing
Gu, Hong
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2021, 33 (02) : 913 - 940
[39] Asymptotic behavior of solutions of Fisher-KPP equation with free boundary conditions
Cai, Jingjing
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 16 : 170 - 177
[40] Uniqueness and stability of forced waves for the Fisher-KPP equation in a shifting environment ☆
Guo, Jong-Shenq
Guo, Karen
Shimojo, Masahiko
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 247

← 1 2 3 4 5 →