In this paper, we consider the following initial value problem$$U_i'(t) = \sum_{j\in B} J_{i-j}(U_J(t) - U_i(t)) - U_i^p(t),~t\geq 0,~i\in B,$$ $$ U_i(0)=\varphi_i>0;~i\in B.$$where $B$ is a bounded subset of $Zd^$, $ p > 1$, $J_h = (J_i)_{i \in B}$ is a kernel which is nonnegative, symmetric, bounded and $\sum_{j \in Z^d} J_j = 1$. We describe the asymptotic behavior of the solution of the above problem. In this paper, we consider the following initial value problem.
@article{7399,
title = {On the asymptotic behavior for a nonlocal di - doi: 10.5269/bspm.v26i1-2.7399},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v26i1-2.7399},
language = {EN},
url = {http://dml.mathdoc.fr/item/7399}
}
Nabongo, Diabate; Boni, Thédore. On the asymptotic behavior for a nonlocal di - doi: 10.5269/bspm.v26i1-2.7399. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v26i1-2.7399. http://gdmltest.u-ga.fr/item/7399/