On some mathematical aspects of kinetic model equations
Authors:
Lawrence Sirovich and James K. Thurber
Journal:
Quart. Appl. Math. 25 (1967), 175-186
MSC:
Primary 82.45
DOI:
https://doi.org/10.1090/qam/219289
MathSciNet review:
219289
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Abstract: A class of integro-differential equations used in the kinetic theory of gases is investigated. The existence and uniqueness of solutions to the initial value problem associated with these equations is proved under relatively weak conditions. Under somewhat stronger assumptions the validity of the application of Fourier—Laplace transforms to this problem is demonstrated. Finally the asymptotic approach to hydrodynamics is shown.
P. L. Bhatnager, E. P. Gross and M. Krook, Phys. Rev. 94, 511 (1954)
- Eugene P. Gross and E. Atlee Jackson, Kinetic models and the linearized Boltzmann equation, Phys. Fluids 2 (1959), 432–441. MR 112306, DOI https://doi.org/10.1063/1.1724415
- Lawrence Sirovich, Kinetic modeling of gas mixtures, Phys. Fluids 5 (1962), 908–918. MR 144719, DOI https://doi.org/10.1063/1.1706706
L. Sirovich and J. K. Thurber, Sound propagation according to kinetic models, AFOSR-1380, MF-17, IMS, NYU (1961)
- L. Sirovich and J. K. Thurber, Sound propagation according to the kinetic theory of gases, Rarefied Gas Dynamics (Proc. 3rd Internat. Sympos., Palais de l’UNESCO, Paris, 1962) Academic Press, New York, 1963, pp. 159–180. MR 0155508
L. Sirovich and J. K. Thurber, in Rarefied gas dynamics, Academic Press, New York and London, (1965)
- Lawrence Sirovich and James K. Thurber, Propagation of forced sound waves in rarefied gas-dynamics, J. Acoust. Soc. Amer. 37 (1965), 329–339. MR 175570, DOI https://doi.org/10.1121/1.1909331
- Lawrence Sirovich, Dispersion relations in rarefied gas dynamics, Phys. Fluids 6 (1963), 10–20. MR 155507, DOI https://doi.org/10.1063/1.1724496
- Lawrence Sirovich, Formal and asymptotic solutions in kinetic theory, Phys. Fluids 6 (1963), 218–230. MR 157699, DOI https://doi.org/10.1063/1.1706721
L. Sirovich, Phys. Fluids 6, 1428 (1963)
S. Chapman and T. G. Cowling, The mathematical theory of non-uniform gases, Cambridge Univ. Press, London and New York, (1952)
W. Magnus and F. Oberlettinger, Formulas and theorems for the functions of mathematical physics, Chelsea Publ. Co., New York, 1954
- 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
P. L. Bhatnager, E. P. Gross and M. Krook, Phys. Rev. 94, 511 (1954)
E. P. Gross and E. A. Jackson, Phys. Fluids 2, 432 (1959)
L. Sirovich, Phys. Fluids 5, 908 (1962)
L. Sirovich and J. K. Thurber, Sound propagation according to kinetic models, AFOSR-1380, MF-17, IMS, NYU (1961)
L. Sirovich and J. K. Thurber, in Rarefied gas dynamics, Academic Press, New York, (1963)
L. Sirovich and J. K. Thurber, in Rarefied gas dynamics, Academic Press, New York and London, (1965)
L. Sirovich and J. K. Thurber, J. Acoust. Soc. Am. 37, 329 (1965)
L. Sirovich, Phys. Fluids 6, 10 (1963)
L. Sirovich, Phys. Fluids 6, 218 (1963)
L. Sirovich, Phys. Fluids 6, 1428 (1963)
S. Chapman and T. G. Cowling, The mathematical theory of non-uniform gases, Cambridge Univ. Press, London and New York, (1952)
W. Magnus and F. Oberlettinger, Formulas and theorems for the functions of mathematical physics, Chelsea Publ. Co., New York, 1954
L. Sirovich, Initial and boundary value problems in dissipalive gas dynamics, (submitted for publication)
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Article copyright:
© Copyright 1967
American Mathematical Society
