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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [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. Silov, General functions. Vol. I: Properties and operations, Fizmatgiz, Moscow, 1958; English transl., Academic Press, New York, 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 Univ. Press, Cambridge, 1956, pp. 250-351 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. Ryžov, Influence of viscosity and thermal conductivity on propagation of sound impulses, Prikl. Mat. Meh. 30, 296-302 (1966) = J. Appl. Math. Mech. 30, 362-369 (1966) MR 0216810
  • [8] L. Sirovich, Initial and boundary value problems in dissipative gas dynamics, Phys. Fluids 10, 24-34 (1967) MR 0208910
  • [9] L. Sirovich, The asymptotic evaluation of multidimensional integrals, J. Math. Phys. 11, 1365-1374 (1970) MR 0271604
  • [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)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76.35

Retrieve articles in all journals with MSC: 76.35

Additional Information

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

American Mathematical Society