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An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy
Joint Authors
Atifi, Khalid
Boutaayamou, Idriss
Ould Sidi, Hamed
Salhi, Jawad
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-09
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Atifi, Khalid& Boutaayamou, Idriss& Ould Sidi, Hamed& Salhi, Jawad. 2018. An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy. Abstract and Applied Analysis،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1114257
Modern Language Association (MLA)
Atifi, Khalid…[et al.]. An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy. Abstract and Applied Analysis No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1114257
American Medical Association (AMA)
Atifi, Khalid& Boutaayamou, Idriss& Ould Sidi, Hamed& Salhi, Jawad. An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy. Abstract and Applied Analysis. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1114257
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1114257