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• W2952203670 abstract "We consider a linear diffusion equation on $Omega:=mathbb{R}^2setminusbar{Omega_mathcal{O}}$, where $Omega_mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $Gamma:=partialOmega_mathcal{O}$ is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of $mathbb{R}^2$ with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time $t$, we derive an $L^2([0,t];L^2(Gamma))$-bound on the difference in flux on the boundary. Moreover, we derive for all $t>0$ an $L^2(Omega)$-bound and an $L^2([0,t];H^1(Omega))$-bound for the difference of the solutions to the two models." @default.
• W2952203670 created "2019-06-27" @default.
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• W2952203670 date "2014-02-22" @default.
• W2952203670 modified "2023-09-28" @default.
• W2952203670 title "Modelling with measures: Approximation of a mass-emitting object by a point source" @default.
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• W2952203670 hasPublicationYear "2014" @default.
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