Asymptotic behaviour for a nonlocal diffusion equation on a lattice期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Asymptotic behaviour for a nonlocal diffusion equation on a lattice

Authors:	Liviu I. Ignat Julio D. Rossi

Affiliation:	(1) Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain;(2) Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania;(3) Depto. Matemática, FCEyN UBA (1428), Buenos Aires, Argentina

Abstract:	In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, $u^{prime}_{n}(t) = sum_{{jin}{{{mathbb{Z}}}^{d}}} J_{n-j}u_{j}(t)-u_{n}(t)$ with t ≥ 0 and $n in {mathbb{Z}}^{d}$ . We assume that J is nonnegative and verifies $sum_{{n in {mathbb{Z}}}^{d}}J_{n}= 1$ . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.

Keywords:	Mathematics Subject Classification (2000). 35B40 45A05 45M05
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