Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN

2001 ◽  
Vol 157 (2) ◽  
pp. 91-163 ◽  
Author(s):  
François Hamel ◽  
Nikolaï Nadirashvili
Keyword(s):  
Entire Solutions ◽  
Kpp Equation ◽  
Travelling Fronts

scholarly journals Entire solutions of the Fisher–KPP equation on the half line

2019 ◽  
Vol 31 (3) ◽  
pp. 407-422 ◽  
Author(s):  
BENDONG LOU ◽  
JUNFAN LU ◽  
YOSHIHISA MORITA
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Traveling Wave ◽  
Wave Solution ◽  
Dirichlet Boundary ◽  
Entire Solution ◽  
Traveling Wave Solution ◽  
Half Line ◽  
Entire Solutions ◽  
Kpp Equation

In this paper, we study the entire solutions of the Fisher–KPP (Kolmogorov–Petrovsky–Piskunov) equation ut = uxx + f(u) on the half line [0, ∞) with Dirichlet boundary condition at x = 0. (1) For any $c \ge 2\sqrt {f'(0)} $, we show the existence of an entire solution ${{\cal U}^c}(x,t)$ which connects the traveling wave solution φc(x + ct) at t = −∞ and the unique positive stationary solution V(x) at t = +∞; (2) We also construct an entire solution ${{\cal U}}(x,t)$ which connects the solution of ηt = f(η) at t = −∞ and V(x) at t = +∞.

Entire solutions to advective Fisher-KPP equation on the half line

2021 ◽  
Vol 305 ◽  
pp. 103-120
Author(s):  
Bendong Lou ◽  
Jinzhe Suo ◽  
Kaiyuan Tan
Keyword(s):  
Half Line ◽  
Entire Solutions ◽  
Kpp Equation

Entire solutions in the Fisher-KPP equation with nonlocal dispersal

2010 ◽  
Vol 11 (4) ◽  
pp. 2302-2313 ◽  
Author(s):  
Wan-Tong Li ◽  
Yu-Juan Sun ◽  
Zhi-Cheng Wang
Keyword(s):  
Entire Solutions ◽  
Nonlocal Dispersal ◽  
Kpp Equation

Entire solutions of time periodic Fisher–KPP equation on the half line

2020 ◽  
Vol 200 ◽  
pp. 112005
Author(s):  
Jingjing Cai ◽  
Li Xu ◽  
Yuan Chai
Keyword(s):  
Half Line ◽  
Entire Solutions ◽  
Kpp Equation ◽  
Time Periodic

Entire solutions of reaction—diffusion equations with balanced bistable nonlinearities

2006 ◽  
Vol 136 (6) ◽  
pp. 1207-1237 ◽  
Author(s):  
Xinfu Chen ◽  
Jong-Shenq Guo ◽  
Hirokazu Ninomiya
Keyword(s):  
Diffusion Equation ◽  
Finite Time ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Entire Solutions ◽  
Stable Equilibria ◽  
Travelling Fronts

This paper deals with entire solutions of a bistable reaction—diffusion equation for which the speed of the travelling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two travelling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a quasi-invariant manifold approach. Such solutions are shown to be unique up to space and time translations.

Sign in / Sign up

Export Citation Format

Share Document