Signal Resoration after Transmission thru an Advective and Diffusive Medium
Paul R. Shorten and David J.N. Wall
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Abstract
Inverse problem, regularisation, singular perturbation, wave splitting, wave propagators, square root operator, inverse mass transport This paper considers an inverse problem associated with mass transport in a pipe. It illustrates how wave splitting techniques can be utilised for an inverse problem associated with one-dimensional mass transport processes. This is done by using a generalisation of Fick's law which introduces a relaxation parameter into the problem, so converting the parabolic partial differential equation by a singular perturbation into a hyperbolic one. This generalised law by ensuring finite mass flux propagation speeds, enables a stable equation to be utilised to reconstruct the interior boundary condition; so providing a regularised solution to the inverse problem. Theoretical results for the solution of the inverse problem are also developed.
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