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

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On the Bateman–Hörmander Solution of the Wave Equation Having a Singularity at a Running Point. / Blagoveshchensky, A. S.; Tagirdzhanov, A. M.; Kiselev, A. P.

In: Journal of Mathematical Sciences (United States), Vol. 243, No. 5, 01.12.2019, p. 682-688.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{8389935caf904ffe8c0600b66f86b0a0,

title = "On the Bateman–H{\"o}rmander Solution of the Wave Equation Having a Singularity at a Running Point",

abstract = "H{\"o}rmander 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 H{\"o}rmander solution is a specialization of a solution found by Bateman five decades in advance.",

author = "Blagoveshchensky, {A. S.} and Tagirdzhanov, {A. M.} and Kiselev, {A. P.}",

year = "2019",

month = dec,

day = "1",

doi = "10.1007/s10958-019-04569-3",

language = "English",

volume = "243",

pages = "682--688",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - On the Bateman–Hörmander Solution of the Wave Equation Having a Singularity at a Running Point

AU - Blagoveshchensky, A. S.

AU - Tagirdzhanov, A. M.

AU - Kiselev, A. P.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074979042&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04569-3

DO - 10.1007/s10958-019-04569-3

M3 - Article

AN - SCOPUS:85074979042

VL - 243

SP - 682

EP - 688

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 73298537