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.
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
- I. M. Gel’fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Academic Press, New York-London, 1964. Translated by Eugene Saletan. MR 0166596
I. S. Gradsteǐn, and I. M. Ryžik, Tables of integrals, series and products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965.
W. D. Hayes, Gasdynamic discontinuities, Princeton Aeronautical Paperbacks, Princeton, N. J., 1960
- 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
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)
- 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, DOI https://doi.org/10.1016/0021-8928%2867%2990183-9
- Lawrence Sirovich, Initial and boundary value problems in dissipative gas dynamics, Phys. Fluids 10 (1967), 24–34. MR 208910, DOI https://doi.org/10.1063/1.1761987
- Lawrence Sirovich, Asymptotic evaluation of multidimensional integrals, J. Mathematical Phys. 11 (1970), 1365–1374. MR 271604, DOI https://doi.org/10.1063/1.1665269
C. H. Su and G. S. Gardner, Derivation of the Korteweg de Vries equation and Burgers equation, J. Math. Phys. 10, 536–539 (1969)
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
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
I. S. Gradsteǐn, and I. M. Ryžik, Tables of integrals, series and products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965.
W. D. Hayes, Gasdynamic discontinuities, Princeton Aeronautical Paperbacks, Princeton, N. J., 1960
M. J. Lighthill, Viscosity effects in sound waves of finite amplitude, Surveys in Mechanics, Cambridge Univ. Press, Cambridge, 1956, pp. 250–351
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)
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)
L. Sirovich, Initial and boundary value problems in dissipative gas dynamics, Phys. Fluids 10, 24–34 (1967)
L. Sirovich, The asymptotic evaluation of multidimensional integrals, J. Math. Phys. 11, 1365–1374 (1970)
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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© Copyright 1971
American Mathematical Society
