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

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.