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Very Weak Solution of the Wave Equation for Sturm-Liouville Operator

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Modern Problems in PDEs and Applications (MWCAPDE 2023)

Part of the book series: Trends in Mathematics ((RPGAPC,volume 4))

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Abstract

We considered the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with singular coefficients. The method of separation of variables is used to construct the solution. The homogeneous and non-homogeneous cases of the equation are considered. Finally, existence, uniqueness, and consistency theorems are given for a very weak solution of the wave equation with singular coefficients in a bounded domain.

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Acknowledgements

The author is supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). Also, the author expresses his gratitude to Professor M. Ruzhansky for his valuable advice.

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Authors and Affiliations

  1. Altynsarin Arkalyk pedagogical Institute, Arkalyk, Kazakhstan

    Alibek Yeskermessuly

Authors
  1. Alibek Yeskermessuly
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Ghent University, Ghent, Belgium

    Marianna Chatzakou

  2. Department of Mathematics, Ghent University, Ghent, Belgium

    Joel Restrepo

  3. Department of Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

  4. Ghent Analysis and PDE Center, Ghent University, Ghent, Belgium

    Berikbol Torebek

  5. Ghent Analysis and PDE Center, Ghent University, Ghent, Belgium

    Karel Van Bockstal

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Yeskermessuly, A. (2024). Very Weak Solution of the Wave Equation for Sturm-Liouville Operator. In: Chatzakou, M., Restrepo, J., Ruzhansky, M., Torebek, B., Van Bockstal, K. (eds) Modern Problems in PDEs and Applications. MWCAPDE 2023. Trends in Mathematics(), vol 4. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-56732-2_17

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