An inversion method for parabolic equations based on quasireversibility |
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Affiliation: | Department of Mechanical Engineering, University of Colorado at Denver Campus Box 112, P.O. Box 173364 Denver, CO 80217-3364, U.S.A.;Department of Mathematics. University of North Carolina at Charlotte Charlotte, NC 28223, U.S.A. |
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Abstract: | This paper is concerned with a new method to solve a linearized inverse problem for one-dimensional parabolic equations. The inverse problem seeks to recover the subsurface absorption coefficient function based on the measurements obtained at the boundary. The method considers a temporal interval during which time dependent measurements are provided. It linearizes the working equation around the system response for a background medium. It is then possible to relate the inverse problem of interest to an ill-posed boundary value problem for a differential-integral equation, whose solution is obtained by the method of quasireversibility. This approach leads to an iterative method. A number of numerical results are presented which indicate that a close estimate of the unknown function can be obtained based on the boundary measurements only. |
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