On the asymptotic behavior for a nonlocal difusion equation with an absorption term on a lattice

Abstract

In this paper, we consider the following initial value problem:U_i'(t) =sum_{jin B} J_{i-j}(U_j(t) - U_i(t)), t geq 0, iin BU_i(0)=varphi_i >0, iin Bwhere B is a bounded subset of Z^d, p > 1, J_ h = (J_i)_{iinB} is a kernel which is nonnegative, symmetric, bounded and sum_{j in Z^d} Jj = 1. We describe the asymptotic behavior of the solution of the above problem.

Keywords

• Nonlocal diffusion
• asymptotic behavior.