Geodesic
Asymptotics of the Solution of an Initial--Boundary Value Problem for the One-Dimensional Klein--Gordon Equation on the Half-Line
Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 602-614.

Voir la notice de l'article provenant de la source Math-Net.Ru

The initial–boundary value problem for the Klein–Gordon equation on the semiaxis is considered. It is possible to reduce to this problem a one-dimensional system of equations of hydrothermodynamics, which describes the motion of atmospheric gas, in particular, the propagation of plane acoustic waves initiated by a source at the lower boundary of the region. An exact analytical solution is obtained, and its asymptotics is constructed.
Keywords: initial–boundary value problem, wave equation, asymptotics.
Mots-clés : Klein–Gordon equation 
@article{MZM_2023_114_4_a8,
     author = {E. S. Smirnova},
     title = {Asymptotics of the {Solution} of an {Initial--Boundary} {Value} {Problem} for the {One-Dimensional} {Klein--Gordon} {Equation} on the {Half-Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {602--614},
     publisher = {mathdoc},
     volume = {114},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a8/}
}
TY  - JOUR
AU  - E. S. Smirnova
TI  - Asymptotics of the Solution of an Initial--Boundary Value Problem for the One-Dimensional Klein--Gordon Equation on the Half-Line
JO  - Matematičeskie zametki
PY  - 2023
SP  - 602
EP  - 614
VL  - 114
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a8/
LA  - ru
ID  - MZM_2023_114_4_a8
ER  - 
%0 Journal Article
%A E. S. Smirnova
%T Asymptotics of the Solution of an Initial--Boundary Value Problem for the One-Dimensional Klein--Gordon Equation on the Half-Line
%J Matematičeskie zametki
%D 2023
%P 602-614
%V 114
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a8/
%G ru
%F MZM_2023_114_4_a8
E. S. Smirnova. Asymptotics of the Solution of an Initial--Boundary Value Problem for the One-Dimensional Klein--Gordon Equation on the Half-Line. Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 602-614. http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a8/

[1] A. N. Tikhonov, A. A. Samarskii, Uravneniya matematicheskoi fiziki, Nauka, M., 1977 | MR

[2] M. V. Fedoryuk, Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[3] S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Effektivnye asimptotiki reshenii zadachi Koshi s lokalizovannymi nachalnymi dannymi dlya lineinykh sistem differentsialnykh i psevdodifferentsialnykh uravnenii”, UMN, 76:5 (461) (2021), 3–80 | DOI | MR | Zbl

[4] A. A. Tolchennikov, “O povedenii resheniya uravneniya Kleina–Gordona s lokalizovannym nachalnym usloviem”, TMF, 199:2 (2019), 330–340 | DOI | MR

[5] S. Leble, E. Smirnova, “Tsunami-launched acoustic wave in the layered atmosphere: explicit formulas including electron density disturbances”, Atmosphere, 10 (2019), 629 | DOI

[6] L. M. Brekhovskikh, O. A. Godin, Akustika sloistykh sred, Nauka, M., 1989

[7] J. Pedloski, Geophysical Fluid Dynamics, Springer-Verlag, New York, 1987

[8] S. Leble, A. Perelomova, “Problem of proper decomposition and initialization of acoustic and entropy modes in a gas affected by the mass force”, Appl. Math. Model., 37:3 (2013), 629–635 | DOI | MR

[9] A. Perelomova, “Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere”, Acta Acust. United Acust., 84 (1998), 1002–1006