Abstract

Asymptotic solutions of the Cauchy problem with localized initial conditions are described for a hyperbolic equation describing waves in a channel of variable cross section. It is shown that, if the equation is reduced to a wave equation, then the solution remains localized, whereas, if the initial equation reduces to the Klein–Gordon equation, then nonlocalized corrections occur in the asymptotics.

中文翻译：

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具有可变系数的双曲方程的渐近解的局部化和扩展，该双曲方程描述了在变截面通道中的波动。

摘要

针对描述可变截面通道中的波浪的双曲方程，描述了具有局部初始条件的柯西问题的渐近解。结果表明，如果方程简化为波动方程，则解保持局部化，而如果初始方程简化为Klein-Gordon方程，则渐近现象会发生非局部校正。