Open Access
2018 An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy
Khalid Atifi, Idriss Boutaayamou, Hamed Ould Sidi, Jawad Salhi
Abstr. Appl. Anal. 2018: 1-16 (2018). DOI: 10.1155/2018/2067304


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.


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Khalid Atifi. Idriss Boutaayamou. Hamed Ould Sidi. Jawad Salhi. "An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy." Abstr. Appl. Anal. 2018 1 - 16, 2018.


Received: 23 August 2018; Accepted: 28 November 2018; Published: 2018
First available in Project Euclid: 10 January 2019

zbMATH: 07029283
MathSciNet: MR3894337
Digital Object Identifier: 10.1155/2018/2067304

Rights: Copyright © 2018 Hindawi

Vol.2018 • 2018
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