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The Wavelet-Based Integral Formula for the Solutions of the Wave Equation in an Inhomogeneous Medium: Convergence of Integrals

In: Integral Methods in Science and Engineering

Author

Listed:
  • E. A. Gorodnitskiy

    (Saint Petersburg State University)

  • M. V. Perel

    (Saint Petersburg State University)

Abstract

An integral representation of the solution of the wave equation in a half-plane filled with an inhomogeneous medium is investigated. This representation gives a decomposition of the solution in terms of exact localized solutions of the same equation (elementary solutions). The representation is constructed by the methods of the Poincaré affine wavelet analysis. The convergence of the fourfold integral of the representation in the parameter space is proved under some assumptions about estimates of elementary solutions.

Suggested Citation

  • E. A. Gorodnitskiy & M. V. Perel, 2022. "The Wavelet-Based Integral Formula for the Solutions of the Wave Equation in an Inhomogeneous Medium: Convergence of Integrals," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 113-125, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_8
    DOI: 10.1007/978-3-031-07171-3_8
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