Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time
Anatoly Anikinab, Sergey Dobrokhotovab, Vladimir Nazaikinskiiab
a Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow
Region, 141701, Russia
b Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo, 101-1, Moscow,
We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The right-hand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the shore as a square root of the distance to the shore, that is, the wave equation has a singularity on the curve. This curve determines the boundary of the domain where the problem is studied. The main result of the paper is efficient asymptotic formulas for the solution of this problem, including the neighborhood of the shore.
Key words and phrases:
wave equation, asymptotic solution, Maslov's canonical operator.
|Russian Science Foundation
|This work is supported by Russian Science Foundation, project No. 16-11-10282.
PDF file (559 kB)
MSC: 34E20, 35L05, 35Q35
Anatoly Anikin, Sergey Dobrokhotov, Vladimir Nazaikinskii, “Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time”, Zh. Mat. Fiz. Anal. Geom., 14:4 (2018), 393–405
Citation in format AMSBIB
\by Anatoly~Anikin, Sergey~Dobrokhotov, Vladimir~Nazaikinskii
\paper Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time
\jour Zh. Mat. Fiz. Anal. Geom.
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