Asymptotic behavior of solutions to nonlocal diffusion systems driven by systems of ordinary differential equations. (English) Zbl 1156.35324

The unique solvability of the initial-boundary value problem of nonlocal diffusion system is established and the asymptotic behaviour of solutions is discussed by means of some key estimates in the first part of the article. The second part of this paper 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 predator-prey model and competitive interaction for two species are taken as fundamental examples of reaction kinetics in order to illustrate our results. Finally, the stability and asymptotic behaviour of solutions of these ecological models are analysed.


35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
92D25 Population dynamics (general)
45K05 Integro-partial differential equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)