Infinite-modal approximate solutions of the Bryan-Pidduck equation |
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| Author |
hukalov@ilt.kharkov.ua1, gordevskyy2006@gmail.com2
1) B. Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine; 2) V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
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| Abstract |
The nonlinear integro-differential Bryan-Pidduck equation for a model of rough spheres is
considered. An approximate solution is constructed in the form of an infinite linear combination
of some Maxwellian modes with coefficient functions that depend on time and spatial
coordinate. Sufficient conditions for the infinitesimality of the uniformly-integral error between
the parts of the Bryan-Pidduck equation are obtained.
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| Keywords |
Bryan-Pidduck equation; rough spheres; uniform-integral error; infinite-modal approximate solutions;
global Maxwellian; screws
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| DOI |
doi:10.15330/ms.49.1.95-108
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| Reference |
1. S. Chapman, T.G.Cowling, The mathematical theory of non-uniform gases, Cambridge Univ. Press,
Cambridge, 1952.
2. C. Cercignani, M. Lampis, On the kinetic theory of a dense gas of rough spheres, J. Statist. Phys., 53 (1988), 655–672. 3. V.D. Gordevskyy, Explicit approximate solutions of the Boltzmann equation for the model of rough spheres, Reports of the National Academy of Sciences of Ukraine, 4 (2000), 10–13. (in Ukrainian) 4. V.D. Gordevskyy, Approximate billow solutions of the kinetic Bryan-Pidduck equation, Math. Meth. Appl. Sci., 23 (2000), 1121–1137. 5. V.D. Gordevskyy, A.A. Gukalov, Maxwell distributions in a model of rough spheres, Ukr. Mat. Zh., 63 (2011), ¹5, 629–639. (in Russian) 6. C. Cercignani, The Boltzman Equation and its Applications, Springer, New York, 1988. 7. T. Carleman, Problems Mathematiques dans la Theorie Cinetique des Gas, Almqvist & Wiksells, Uppsala, 1957. 8. H. Grad, On the kinetic theory of rarefield gases, Comm. Pure and Appl. Math., 2 (1949), ¹4, 331–407. 9. O.G. Fridlender, Local Maxwellian Solutions of the Boltzmann Equation, J. Appl. Math. Mech., 29 (1965), ¹5, 973–977. (in Russian) 10. V.D. Gordevskyy, On the non-stationary Maxwellians, Math. Meth. Appl. Sci., 27 (2004), ¹2, 231–247. 11. V.D. Gordevskyy, Biflow distributions with screw modes, Theor. Math. Phys., 126 (2001), ¹2, 234–249. 12. A.A. Gukalov, Interaction between ”Accelarating-Packing” Flows for the Bryan-Pidduck Model, J. of Math. Phys., Anal., Geometry, 9 (2013), ¹3, 316–331. 13. V.D. Gordevskyy, Approximate Biflow Solutions of the Kinetic Bryan-Pidduck Equation, Math. Meth. Appl. Sci., 23 (2003), 1121–1137. 14. V.D. Gordevskyy, A.A. Gukalov, Interaction of the Eddy Flows in the Bryan–Pidduck Model, Vysnik Kharkiv Univ., Ser. Mat. Prykl. Mat. Mech., 64 (2011), ¹2, 27–41. (in Russian) |
| Pages |
95-108
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| Volume |
49
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| Issue |
1
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| Year |
2018
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |