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

C2 - 25811438

VL - 12

SP - 357

EP - 373

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -