An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additio...

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Bibliographic Details
Main Authors: Khalid Atifi, Idriss Boutaayamou, Hamed Ould Sidi, Jawad Salhi
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2018/2067304
Description
Summary:The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.
ISSN:1085-3375
1687-0409