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Inversion theory for a parameterized diffusion problem. (English) Zbl 0664.35075

The author considers the problem \[ \partial^ 2E(z,w)/\partial z^ 2=i\mu_ 0w \sigma (z)E(z,w),\quad \sigma (z)>0,\quad E(-D,w)=0,\quad E(0,w)=1,\quad D>0, \] which is commonly used to describe the one- dimensional magnetotelluric problem. It is shown that for a large space of conductivity functions (with no analyticity requirements), the conductivity function is uniquely recoverable from magnetotelluric data.
Reviewer: D.E.Edmunds

MSC:

35R30 Inverse problems for PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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