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

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

Research output: Book/ReportReportAcademic

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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.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages13
Publication statusPublished - 2014

Publication series

NameCASA-report
Volume1403
ISSN (Print)0926-4507

Fingerprint

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

Cite this

Evers, J. H. M., Hille, S. C., & Muntean, A. (2014). Modelling with measures : approximation of a mass-emitting object by a point source. (CASA-report; Vol. 1403). Eindhoven: Technische Universiteit Eindhoven.
Evers, J.H.M. ; Hille, S.C. ; Muntean, A. / Modelling with measures : approximation of a mass-emitting object by a point source. Eindhoven : Technische Universiteit Eindhoven, 2014. 13 p. (CASA-report).
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Evers, JHM, Hille, SC & Muntean, A 2014, Modelling with measures : approximation of a mass-emitting object by a point source. CASA-report, vol. 1403, Technische Universiteit Eindhoven, Eindhoven.

Modelling with measures : approximation of a mass-emitting object by a point source. / Evers, J.H.M.; Hille, S.C.; Muntean, A.

Eindhoven : Technische Universiteit Eindhoven, 2014. 13 p. (CASA-report; Vol. 1403).

Research output: Book/ReportReportAcademic

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N2 - 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.

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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Evers JHM, Hille SC, Muntean A. Modelling with measures : approximation of a mass-emitting object by a point source. Eindhoven: Technische Universiteit Eindhoven, 2014. 13 p. (CASA-report).