Convergence of nonlocal diffusion models on lattices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:415

Article

Thompson, Stephen

关键词: Neumann fractional Laplacian;    Anomalous diffusion;    Continuum limit;    Trotter-Kato theorem;   

DOI  :  10.1016/j.jmaa.2014.01.062

来源: Elsevier

【 摘 要 】

In this paper we look at models of nonlocal (or anomalous) diffusion which are defined on subsets of the lattice is an element of Zeta(n), for some is an element of > 0, and ask if they can be approximated by continuum models. The answer is given by an operator semigroup convergence theorem. As an application, we establish hypotheses under which a discrete model of nonlocal diffusion satisfying an absorbing boundary condition has a continuum limit which is conservative. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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