Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the structure of dissipative waves in two and three dimensions

Authors: Lorne Halabisky and Lawrence Sirovich
Journal: Quart. Appl. Math. 29 (1971), 135-149
MSC: Primary 76.35
DOI: https://doi.org/10.1090/qam/286361
MathSciNet review: 286361
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Abstract: The problem of two- and three-dimensional small disturbances in a dissipative gas is considered. Explicit forms in terms of known functions are obtained for the time-asymptotic theory in each case. Although the far field solutions may be nonlinear in one dimension, they are always self-consistently linear for two and three dimensions.

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  • [1] M. Abramowitz and I. A. Stegun (editors), Handbook of mathematical functions, with formulas, graphs and mathematical tables, Nat. Bur. Standards Appl. Math. Series, 55, U.S. Government Printing Office, Washington, D.C., 1964
  • [2] I. M. Gel’fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Translated by Eugene Saletan, Academic Press, New York-London, 1964. MR 0166596
  • [3] I. S. Gradstein, and I. M. Ryžik, Tables of integrals, series and products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965.
  • [4] W. D. Hayes, Gasdynamic discontinuities, Princeton Aeronautical Paperbacks, Princeton, N. J., 1960
  • [5] M. J. Lighthill, Viscosity effects in sound waves of finite amplitude, Surveys in mechanics, Cambridge, at the University Press, 1956, pp. 250–351 (2 plates). MR 0077346
  • [6] J. P. Moran and S. F. Shen, On the formation of weak plane shock waves by impulsive motion of a piston, J. Fluid Mech. 25, 705-718 (1966)
  • [7] O. S. Ryzhov, Influence of viscosity and thermal conductivity on propagation of sound impulses, J. Appl. Math. Mech. 30 (1966), 362–369 (1967). MR 0216810, https://doi.org/10.1016/0021-8928(67)90183-9
  • [8] Lawrence Sirovich, Initial and boundary value problems in dissipative gas dynamics, Phys. Fluids 10 (1967), 24–34. MR 0208910, https://doi.org/10.1063/1.1761987
  • [9] Lawrence Sirovich, Asymptotic evaluation of multidimensional integrals, J. Mathematical Phys. 11 (1970), 1365–1374. MR 0271604, https://doi.org/10.1063/1.1665269
  • [10] C. H. Su and G. S. Gardner, Derivation of the Korteweg de Vries equation and Burgers equation, J. Math. Phys. 10, 536-539 (1969)

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DOI: https://doi.org/10.1090/qam/286361
Article copyright: © Copyright 1971 American Mathematical Society

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