title: Modelling with measures: approximation of a mass-emitting object by a point source.
abstract: We consider a linear diffusion equation on Ω: = R(2) \ Ω[Symbol: see text], where Ω[Symbol: see text] is a bounded domain. The time-dependent flux on the boundary Γ: = ∂ Ω[Symbol: see text] 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];L2(Γ))-bound on the difference in flux on the boundary. Moreover, we derive for all t > 0 an L(2)(Ω)-bound and an L2([0,t];H(1)(Ω))-bound for the difference of the solutions to the two models.
authors: Institute for Complex Molecular Systems and Centre for Analysis, Scientific computing and Applications, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands. j.h.m.evers@tue.nl.
authors: Joep H M
authors: JH
authors: Evers
authors: Sander C
authors: SC
authors: Hille
authors: Adrian
authors: A
authors: Muntean
mesh_terms: D000465:Algorithms; D003102:Colloids; D060733:Electromagnetic Radiation; D015233:Models, Statistical; D008962:Models, Theoretical; D009068:Movement; D010825:Physics; D013997:Time Factors
chemical_list: D003102:Colloids