| | |
| | |
Stat |
Members: 3667 Articles: 2'599'751 Articles rated: 2609
08 February 2025 |
|
| | | |
|
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 | Abstract: | In 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 |
|
|
No review found.
Did you like this article?
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.
|
| |
|
|
|