Time-periodic solutions of the boltzmann equation

Discrete and Continuous Dynamical Systems

Volumn 14, Issue 3, 2006, Pages 579-596

  Ukai, Seiji ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Asymptotic stability; Boltzmann equation; Stationary solution; Time decay estimate; Time periodic solution

Indexed keywords

EID: 33644525007     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.14.579     Document Type: Article

References (23)

1. H. Amann, Periodic solutions of semi-linear parabolic equations, Nonlinear Analysis, Academic Press, New York, 1978, pp. 1-29.
2. V. Barbu, Periodic solutions to unbounded Hamiltonian system, Discrete and Continuous Dynamical Systems, 1(1995), 277-283.
3. C.Cercignani, "Theory and Application of the Boltzmann Equation," Elsevier, Amsterdam, 1975.
4. C.Cercignani, R.Illner and M.Pluvirenti, "The Mathematical Theory of Dilute Gases," Appl. Math. Sci. Vol. 109, Springer-Verlag, New-York-Berlin, 1994.
5. G. Cordaro, Existence and location of periodic solutions to convex and non coercive Hamiltonian system, Discrete and Continuous System -Series A, 12(2005), 983-996.
6. H.Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. Appl. Math. 17 (ed. R.Finn), pp. 154-183, AMS, Providence, 1963.
7. P. Hess, On positive solutions of semi-linear periodic-parabolic problems, in "Infinite-Dimensional Systems" (ed. F. Kappel and W. Schappacher), Lecture Notes in Mathematics, vol. 1076, Springer-Verlag, Berlin, 1994, pp. 101-122.
8. n with applications to weak solutions, Math. Z., 187(1984), 471-480.
9. S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math., 34 (1981), 481-524.
10. L. D. Landau and E. M. Lifshitz, "Fluid Mechanics," Pergamon, Oxford, 1987.
11. A. Matsumura and T. Nishida, Periodic solutions of a viscous gas equation, in "Recent topics in nonlinear PDE, IV (Kyoto, 1988)," (ed. K. Masuda and M. Mimura,) pp. 49-82, North-Holland Math. Stud., 160, North-Holland, Amsterdam, 1989.
12. J. Mawhin and J. R. Ward Jr, Guiding-like functions for periodic or bounded solutions of ordinary differential equations, Discrete and Continuous Dynamical System - Series A, 8(2002), 39-54.
13. J. J. Morgan and S. L. Hollis, The existence of periodic solutions to reaction diffusion systems with periodic data, SIAM J. Math. Anal., 26(1995), 1225-1232.
14. M. N. Nkashama, Semi-linear periodic-parabolic equations with nonlinear boundary conditions, J. Differential Equations, 130(1996), 377-405.
15. S. Takeno, Time-periodic solutions for a scalar conservation law. Nonlinear Analysis, 45(2001), 1039-1060.
16. P. J. Torres, Non-collision periodic solutions of forced dynamical systems with weak singularities, Discrete and Continuous System -Series A, 11(2004), 693-698.
17. S. Ukai, On the existence of global solutions of mixed problem for Non-linear Boltzmann equation, Proc. Japan Acad., 50(1974),179-184.
18. S. Ukai, Les solutions globales de l'équation de Boltzmann dans l'espace tout entier et dans le demi-espace, C. R. Acad. Sci. Paris, 282A(1976), 317-320.
19. S. Ukai, Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff, Japan. J. Appl. Math., 1(1985), 141-156.
20. S. Ukai, Solutions of the Boltzmann equation, in "Pattern and Waves - Qualitative Analysis of Nonlinear Differential Equations," (ed. M.Mimura and T.Nishida), Studies of Mathematics and Its Applications 18, Kinokuniya-North-Holland, Tokyo, 1986, pp. 37-96.
21. n, Comm. Pure Appl. Math., XL(1987), 611-621.
22. S. Ukai, Periodic solutions of the Boltzmann equation, Tagungsbericht 47/1999, Nonlinear Equations in Many-Particle Systems, 05.12.-11.12.1999, Mathematishes Forschungsinstitut Oberwolfach, 1999, p.15.
23. Z. Wang, Periodic solutions of the second order differential equations with asymmetric non-linearities depending on the derivatives, Discrete and Continuous Dynamical Systems - Series A, 9(2003), 751-770.