Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3667
Articles: 2'599'751
Articles rated: 2609

08 February 2025
 
  » arxiv » 1508.0063

 Article overview



Global existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problem
Shen Bian ; Li Chen ; Evangelos A. Latos ;
Date 1 Aug 2015
AbstractIn this work, we consider a nonlocal Fisher-KPP reaction-diffusion problem with Neumann boundary condition and nonnegative initial data in a bounded domain in $mathbb{R}^n (n ge 1)$, with reaction term $u^alpha(1-m(t))$, where $m(t)$ is the total mass at time $t$. When $alpha ge 1$ and the initial mass is greater than or equal to one, the problem has a unique nonnegative classical solution. While if the initial mass is less than one, then the problem admits a unique global solution for $n=1,2$ with any $1 le alpha <2$ or $n ge 3$ with any $1 le alpha < 1+2/n$. Moreover, the asymptotic convergence to the solution of the heat equation is proved. Finally, some numerical simulations in dimensions $n=1,2$ are exhibited. Especially, for $alpha>2$ and the initial mass is less than one, our numerical results show that the solution exists globally in time and the mass tends to one as time goes to infinity.
Source arXiv, 1508.0063
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.






ScienXe.org
» my Online CV
» Free

home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2025 - Scimetrica