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

J.H.M. Evers, S.C. Hille, A. Muntean

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Abstract

We consider a linear diffusion equation on O := R^2 \ O_O, where O_O is a bounded domain. The (time-dependent) flux on the boundary G := dO_O is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of 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(G))-bound on the difference in flux on the boundary. Moreover, we derive for all t an L^2(O)-bound and an L^2(0,t; H^1(O))-bound for the difference of the solutions to the two models. Keywords : Point source, model reduction, boundary exchange, diffusion, quantitative flux estimates, modelling with measures.
LanguageEnglish
Pages357-373
Number of pages17
JournalMathematical Biosciences and Engineering
Volume12
Issue number2
DOIs
StatePublished - 2015

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Point Source
Diffusion equation
Approximation
Modeling
Fluxes
Linear Diffusion
Model Reduction
Estimate
Bounded Domain
Linear equation
Ion exchange
Object
Model

Cite this

Evers, J.H.M. ; Hille, S.C. ; Muntean, A./ Modelling with measures : approximation of a mass-emitting object by a point source. In: Mathematical Biosciences and Engineering. 2015 ; Vol. 12, No. 2. pp. 357-373
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Modelling with measures : approximation of a mass-emitting object by a point source. / Evers, J.H.M.; Hille, S.C.; Muntean, A.

In: Mathematical Biosciences and Engineering, Vol. 12, No. 2, 2015, p. 357-373.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - We consider a linear diffusion equation on O := R^2 \ O_O, where O_O is a bounded domain. The (time-dependent) flux on the boundary G := dO_O is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of 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(G))-bound on the difference in flux on the boundary. Moreover, we derive for all t an L^2(O)-bound and an L^2(0,t; H^1(O))-bound for the difference of the solutions to the two models. Keywords : Point source, model reduction, boundary exchange, diffusion, quantitative flux estimates, modelling with measures.

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