Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/58215
Title: Approximation of random diffusion equations by nonlocal diffusion equations in free boundary problems of one space dimension
Contributor(s): Du, Yihong  (author)orcid ; Ni, Wenjie  (author)orcid 
Publication Date: 2022
DOI: 10.1142/S0219199722500043
Handle Link: https://hdl.handle.net/1959.11/58215
Abstract: 

We show how the Stefan type free boundary problem with random diffusion in one space dimension can be approximated by the corresponding free boundary problem with nonlocal diffusion. The approximation problem is a slightly modified version of the nonlocal diffusion problem with free boundaries considered in [J. Cao, Y. Du, F. Li and W.-T. Li, The dynamics of a Fisher–KPP nonlocal diffusion model with free boundaries, J. Functional Anal. 277 (2019) 2772–2814" C. Cortazar, F. Quiros and N. Wolanski, A nonlocal diffusion problem with a sharp free boundary, Interfaces Free Bound. 21 (2019) 441–462]. The proof relies on the introduction of several auxiliary free boundary problems and constructions of delicate upper and lower solutions for these problems. As usual, the approximation is achieved by choosing the kernel function in the nonlocal diffusion term of the form Jϵ(x)=1ϵJ(xϵ) for small ϵ>0 , where J(x) has compact support. We also give an estimate of the error term of the approximation by some positive power of ϵ.

Publication Type: Journal Article
Source of Publication: Communications in Contemporary Mathematics, 25(4), p. 1-42
Publisher: World Scientific Publishing Co Pte Ltd
Place of Publication: Singapore
ISSN: 1793-6683
0219-1997
Fields of Research (FoR) 2020: 4904 Pure mathematics
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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