Journal of Applied Mathematics and Decision Sciences 
Volume 5 (2001), Issue 2, Pages 87-104
doi:10.1155/S1173912601000086

Fluid velocity profile reconstruction for non-Newtonian shear dispersive flow

Paul R. Shorten and David J. N. Wall

 Biomathematics Research Centre, Department of Mathematics & Statistics, University of Canterbury, Christchurch, 1, New Zealand

Abstract

An inverse problem associated with the mass transport of a material concentration down a pipe where the flowing non-Newtonian medium has a two-dimensional velocity profile is examined. The problem of determining the two-dimensional fluid velocity profile from temporally varying cross-sectional average concentration measurements at upstream and downstream locations is considered. The special case of a known input upstream concentration with a time zero step, and a strictly decreasing velocity profile is shown to be a well-posed problem. This inverse problem is in general ill-posed and mollification is used to obtain a well conditioned problem.