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 -