Abstract:
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, Klein–Gordon equation, wave equation, asymptotics.
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