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On the Determination of Point-Forces on a Stokes System

Alves, Carlos J. S.; Silvestre, Ana Leonor

Mathematics and Computers in Simulation, 66(4-5) (2004), 385-397

We consider the steady Stokes equations in a bounded domain Omega subset of R-n, n = 2, 3 describing the motion of an incompressible viscous fluid under the action of point-forces located inside Omega. The objective of this work is to solve the inverse problem of determining the number, location and strength of the these point-forces. The detection of the unknown point-forces is made by means of the prescribed fluid velocity at the boundary partial derivativeOmega and by a single measurement of the stress exerted by the fluid on partial derivativeOmega. The main tool is the use of a reciprocity gap function, which is obtained by applying a reciprocity gap functional to Stokeslets located outside Omega. This procedure leads to the resolution of a nonlinear minimization problem. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.