### Abstract

Language | English |
---|---|

Pages | 357-373 |

Number of pages | 17 |

Journal | Mathematical Biosciences and Engineering |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 2015 |

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*Mathematical Biosciences and Engineering*,

*12*(2), 357-373. DOI: 10.3934/mbe.2015.12.357

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*Mathematical Biosciences and Engineering*, vol. 12, no. 2, pp. 357-373. DOI: 10.3934/mbe.2015.12.357

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

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Modelling with measures : approximation of a mass-emitting object by a point source

AU - Evers,J.H.M.

AU - Hille,S.C.

AU - Muntean,A.

PY - 2015

Y1 - 2015

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.

U2 - 10.3934/mbe.2015.12.357

DO - 10.3934/mbe.2015.12.357

M3 - Article

VL - 12

SP - 357

EP - 373

JO - Mathematical Biosciences and Engineering

T2 - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -