Email this article On the Bateman–Hörmander Solution of the Wave Equation Having a Singularity at a Running Point
- Authors: Blagoveshchensky A.S.1, Tagirdzhanov A.M.1,2, Kiselev A.P.3,4
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Affiliations:
- St. Petersburg State University
- St. Petersburg Electrotechnical University
- St. Petersburg Department of the Steklov Mathematical Institute
- Institute of Mechanical Engineering RAS
- Issue: Vol 243, No 5 (2019)
- Pages: 682-688
- Section: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/243138
- DOI: https://doi.org/10.1007/s10958-019-04569-3
- ID: 243138
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Abstract
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.
About the authors
A. S. Blagoveshchensky
St. Petersburg State University
Author for correspondence.
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg
A. M. Tagirdzhanov
St. Petersburg State University; St. Petersburg Electrotechnical University
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg; St. Petersburg
A. P. Kiselev
St. Petersburg Department of the Steklov Mathematical Institute; Institute of Mechanical Engineering RAS
Email: a.blagoveshchensky@spbu.ru
Russian Federation, St. Petersburg; St. Petersburg
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