Signal restoration after transmission through an advective and diffusive medium
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.
SubjectsField of Research::01 - Mathematical Sciences::0102 - Applied Mathematics::010202 - Biological Mathematics
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