Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2018 (2018), Article ID 2067304, 16 pages.
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 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.
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 2067304, 16 pages.
Received: 23 August 2018
Accepted: 28 November 2018
First available in Project Euclid: 10 January 2019
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Atifi, Khalid; Boutaayamou, Idriss; Ould Sidi, Hamed; Salhi, Jawad. An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy. Abstr. Appl. Anal. 2018 (2018), Article ID 2067304, 16 pages. doi:10.1155/2018/2067304. https://projecteuclid.org/euclid.aaa/1547089412