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

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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 
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     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},
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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/