Recovery of a one dimensional impedance profile from transmission data

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Date
1993
Authors
Maheswaran, Thiagarajah
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Paul E. Sacks
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Altmetrics
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Mathematics
Abstract

In this thesis we study the problem of recovering the unknown impedance A in the partial differential equation Au[subscript]tt - (Au[subscript]x)[subscript]x = 0, x > 0, t > 0 subject to the boundary condition u[subscript]x(0,t)=-[delta](t) from the measured response u[subscript]t(x,t), 0 < t < 3X at x = X. It is assumed that (UNFORMATTED TABLE OR EQUATION FOLLOWS)\eqalignu = 0, &t < 0 0 < [delta] < A, Aϵ H[superscript]1 & and A[superscript]' = 0, x≥ X. (TABLE/EQUATION ENDS);We present two different iterative methods to recover A from the data u[subscript]t(X,t), 0

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Fri Jan 01 00:00:00 UTC 1993