Translator Disclaimer
2007 Asymptotic behavior of solutions to nonlocal diffusion systems driven by systems of ordinary differential equations
Michel Chipot, Koji Okada
Adv. Differential Equations 12(8): 841-866 (2007).

Abstract

In this article, an initial-/boundary-value problem for a nonlocal diffusion system is treated. In the first part of the article, the unique solvability of the problem is established, and the asymptotic behavior of solutions is discussed by means of some key estimates. For the problem, it is also proved that the corresponding initial-value problem for a system of ordinary differential equations are of crucial importance. The second part of the article is devoted to the analysis of some nonlocal reaction-diffusion systems which are obtained as the special case where the coefficient matrices in the original system are diagonal. Lotka-Volterra prey-predator interaction and competitive interaction for two species are taken as fundamental examples of reaction kinetics; the stability and asymptotic behavior of solutions to these ecological models are inspected.

Citation

Download Citation

Michel Chipot. Koji Okada. "Asymptotic behavior of solutions to nonlocal diffusion systems driven by systems of ordinary differential equations." Adv. Differential Equations 12 (8) 841 - 866, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1156.35324
MathSciNet: MR2340255

Subjects:
Primary: 35K57
Secondary: 34A12, 34C29, 35B35, 35B40

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.12 • No. 8 • 2007
Back to Top