This article is cited in 1 scientific paper (total in 1 paper)
Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem
A. Yu. Anikinab, S. Yu. Dobrokhotovab, V. E. Nazaikinskiiab
a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Asymptotic solutions of the wave equation degenerating on the boundary of the domain (where the wave propagation velocity vanishes as the square root of the distance from the boundary) can be represented with the use of a modified canonical operator on a Lagrangian submanifold, invariant with respect to the Hamiltonian vector field, of the nonstandard phase space constructed by the authors in earlier papers. The present paper provides simple expressions in a neighborhood of the boundary for functions represented by such a canonical operator and, in particular, for the solution of the Cauchy problem for the degenerate wave equation with initial data localized in a neighborhood of an interior point of the domain.
wave equation, nonstandard characteristics, run-up on a sloping beach, localized source, near-boundary asymptotics.
|Russian Science Foundation
|This work was supported
by the Russian Science Foundation
under grant 16-11-10282 in accordance with paragraph 17.7 of Sec. 3.1.
and paragraph (7) of Sec. 3.2 of the work schedule for this grant
for the year 2017.
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Mathematical Notes, 2018, 104:4, 471–488
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem”, Mat. Zametki, 104:4 (2018), 483–504; Math. Notes, 104:4 (2018), 471–488
Citation in format AMSBIB
\by A.~Yu.~Anikin, S.~Yu.~Dobrokhotov, V.~E.~Nazaikinskii
\paper Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem
\jour Mat. Zametki
\jour Math. Notes
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This publication is cited in the following articles:
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”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 393–405
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