IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3186-d1198730.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    Department of Applied Mathematics, National Research Centre, Cairo 12622, Egypt)

  • Rob H. De Staelen

    (Beheer en Algemene Directie, Ghent University Hospital, Corneel Heymanslaan 10, B-9000 Ghent, Belgium
    Research Department, Ghent University, Sint-Pietersnieuwstraat 25, 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
    Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt)

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.

Suggested Citation

  • Hamed Ould Sidi & Mahmoud A. Zaky & Rob H. De Staelen & Ahmed S. Hendy, 2023. "Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy," Mathematics, MDPI, vol. 11(14), pages 1-24, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3186-:d:1198730
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3186/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3186/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Uriel Frisch & Sabino Matarrese & Roya Mohayaee & Andrei Sobolevski, 2002. "A reconstruction of the initial conditions of the Universe by optimal mass transportation," Nature, Nature, vol. 417(6886), pages 260-262, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3186-:d:1198730. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.