Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy

Hamed Ould Sidi, Mahmoud A. Zaky, Rob H. De Staelen () and Ahmed S. Hendy
Additional contact information
Hamed Ould Sidi: Department of Mathematics, Faculty of Sciences, University of Nouakchott Al Aasriya, Nouakchott Bp 6093, Mauritania
Mahmoud A. Zaky: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Rob H. De Staelen: Beheer en Algemene Directie, Ghent University Hospital, Corneel Heymanslaan 10, B-9000 Ghent, Belgium
Ahmed S. Hendy: Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia

Mathematics, 2023, vol. 11, issue 14, 1-24

Abstract: A simultaneous reconstruction of the initial condition and the space-dependent reaction coefficient in a multidimensional hyperbolic partial differential equation with interior degeneracy is of concern. A temporal integral observation is utilized to achieve that purpose. The well-posedness, existence, and uniqueness of the inverse problem under consideration are discussed. The inverse problem can be reformulated as a least squares minimization and the Fréchet gradients are determined, using the adjoint and sensitivity problems. Finally, an iterative construction procedure is developed by employing the conjugate gradient algorithm while invoking the discrepancy principle as a stopping criterion. Some numerical experiments are given to ensure the performance of the reconstruction scheme in one and two dimensions.

Keywords: wave problem; interior degeneracy; coefficient and initial function reconstruction; CGM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/14/3186/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/14/3186/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:14:p:3186-:d:1198730

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().