Modelling with measures: Approximation of a mass-emitting object by a point source

2014/02/22 by Evers, Joep H. M., Hille, Sander C., Muntean, Adrian
#35A35 #35B45 #35K05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.5558

Abstract

We consider a linear diffusion equation on Ω:=ℝ²∖Ω_O, where Ω_O is a bounded domain. The time-dependent flux on the boundary Γ:=∂Ω_O is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of ℝ² with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time t, we derive an L²([0,t];L²(Γ))-bound on the difference in flux on the boundary. Moreover, we derive for all t>0 an L²(Ω)-bound and an L²([0,t];H¹(Ω))-bound for the difference of the solutions to the two models.

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