Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate
Abstract
For an initial-boundary value problem for a parabolic equation in the spatial variable x=(x1,.., xn) and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component xn by extra lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also we prove similar results for the corresponding inverse source problem.
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