THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
ON THE ASYMPTOTIC IN TIME OF SOLUTIONS OF THE BOLTZMANN EQUATION IN THE CASE OF SOFT INTERMOLECULAR POTENTIALS
- ^{1} Institute of Computer Science and Technology – Peter the Great Saint-Petersburg Polytechnic University, Russia
Abstract
The work is devoted to the mathematical problems of the analysis of asymptotic time behavior of solutions of the nonstationary Boltzmann equation. The proof of the fundamental difference between such behavior for the cases of “hard” and “soft” (in the sense of H. Grad) potentials of intermolecular interaction is given
Keywords
References
- Carleman T. Problemes Mathematiques dans la Theorie Cinetique des Gaz. – Uppsala, 1957.
- Maslova N.B. Solvability theorems for the nonlinear Boltzmann equation // Supplement II to the Russian translation of the book: Cercignani K. Theory and Applications of the Boltzmann Equation. – Moscow, 1978, p. 461-480 (in Russian)
- Lebowitz J.L., Montroll E.W. (editors). Nonequilibrium Phenomena: The Boltzmann Equation. – North-Holland Publishing Company, 1983
- Maslova N.B., Firsov A.N. On the General solvability of the Cauchy problem for the nonlinear Boltzmann equation. – Proceedings of the all-Union conference on partial differential equations. Publishing house of Moscow University, Moscow, 1978, p. 376 – 377 (in Russian)
- Firsov A.N. On a Cauchy problem for the nonlinear Boltzmann equation. – Aerodynamics of rarefied gases, issue 8. Publishing House of Leningrad State University, Leningrad, 1976, p. 22 – 37 (in Russian)
- Firsov A.N. Generalized mathematical models and methods for analyzing dynamic processes in distributed systems. – Publishing House of Polytechnic University, St. Petersburg, 2012 (in Russian)
- Caflich R.E. The Boltzmann equation with a soft potential //Commun. Math. phys., 1980, v. 74, p. 71-95.
- Grad H. Asymptotic theory of the Boltzmann equation, II. Rarefied Gas Dynamics, vol. I, Academic Press, New York, London, 1963, p. 26 – 59.
- Hille E., Phillips R.S. Functional Analysis and Semi-Groups. – Providence, 1957.
- Reed M., Simon B. Methods of Modern Mathematical Physics. Vol. II. – Academic Press, NY, San Francisco, London, 1975
- Maslova N.B., Firsov A.N. Solution of the Cauchy problem for the Boltzmann equation. I. // Vestnik of Leningrad University, 1975, № 19, p. 83-88 (in Russian)