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On the Bateman–Hörmander Solution of the Wave Equation Having a Singularity at a Running Point

  • A. S. BlagoveshchenskyEmail author
  • A. M. Tagirdzhanov
  • A. P. Kiselev
Article

Hörmander has presented a remarkable example of a solution of the homogeneous wave equation, which has a singularity at a running point. An analytic investigation of this solution is performed for the case of three spatial variables. The support of this solution is described, its behavior near the singular point is studied, and its local integrability is established. It is observed that the Hörmander solution is a specialization of a solution found by Bateman five decades in advance.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. S. Blagoveshchensky
    • 1
    Email author
  • A. M. Tagirdzhanov
    • 1
    • 2
  • A. P. Kiselev
    • 3
    • 4
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.St. Petersburg Electrotechnical UniversitySt. PetersburgRussia
  3. 3.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  4. 4.Institute of Mechanical Engineering RASSt. PetersburgRussia

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