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标题：A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions
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作者：Cesar A. Gómez ; Julio D. Rossi
期刊名称：Journal of King Saud University - Science
印刷版ISSN：1018-3647
出版年度：2020
卷号：32
期号：1
页码：17-20
DOI：10.1016/j.jksus.2017.08.008
语种：English
出版社：Elsevier
摘要：AbstractIn this paper we discuss a nonlocal approximation to the classical heat equation with Neumann boundary conditions. We considerwt∊(x,t)=1∊N+2∫ΩJx-y∊(w∊(y,t)-w∊(x,t))dy+C1∊N∫∂ΩJx-y∊g(y,t)dSy,(x,t)∈Ω‾×(0,T),w(x,0)=u0(x),x∈Ω‾,and we show that the corresponding solutions,w∊, converge to the classical solution of the local heat equationvt=Δvwith Neumann boundary conditions,∂v∂n(x,t)=g(x,t), and initial conditionv(0)=u0, as the parameter∊goes to zero. The obtained convergence is in the weak star onL∞topology.
关键词：Nonlocal diffusion;Neumann boundary conditions;Heat equation