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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Print: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v31.i4.70
7 pages

Violation of the Solution Superposition Principle for the Initial-Boundary Problem with Mobile Boundaries for Wave Equation

V. A. Pozdeev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv; and Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine

ABSTRACT

Violation of the superposition principle when allowing for moving boundaries, even in the case of a linear wave equation, is shown on an example of analytical solution of the initial-boundary problem on acoustic wave radiation by a moving plane piston. The developed solution for the piston motion, represented as a superposition of low-amplitude oscillations upon the constant velocity, describes the well-known Doppler effect. All results are obtained on the basis of the non-linear time transformation technique.


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