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Uniform asymptotics for the linearized Boltzmann equation describing sound wave propagation

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Abstract

The multiple-scale expansionmethod is used for constructing a uniformly applicable asymptotic approximation of the solution of the linearized Boltzmann equation for small Knudsen numbers. The asymptotic expansion is constructed for the particular example of a sound wave generated by a plane oscillation source and dissipating in a half-space. The simplicity of the problem makes it possible clearly to demonstrate the appearance of secular terms in the expansion and the introduction of multiple scales opens the way to eliminating them.

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Authors
  1. I. B. Chekmarev
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  2. O.M. Chekmareva
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Additional information

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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, 2006, pp. 195–202.

Original Russian Text Copyright © 2006 by Chekmarev and Chekmareva.

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Chekmarev, I.B., Chekmareva, O. Uniform asymptotics for the linearized Boltzmann equation describing sound wave propagation. Fluid Dyn 41, 661–667 (2006). https://doi.org/10.1007/s10697-006-0085-0

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  • DOI: https://doi.org/10.1007/s10697-006-0085-0

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