Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

Archive for Rational Mechanics and Analysis

Volumn 134, Issue 1, 1996, Pages 1-16

  Cercignani, C ^a,b   Illner, R ^a,b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18844472351     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00376253     Document Type: Article

References (18)

1. L. ARKERYD, Existence theorems for certain kinetic equations and large data. Arch. Rational Mech. Anal. 103, 139-149 (1988).
2. 1 trend to equilibrium for the Boltzmann equation. Studies in Appl. Math. 87, 283-288 (1992).
3. L. ARKERYD & C. CERCIGNANI, A global existence theorem for the initial-boundary value problem for the Boltzmann equation when the boundaries are not isothermal. Arch. Rational Mech. Anal. 125, 271-288 (1993).
4. L. ARKERYD, C. CERCIGNANI & R. ILLNER, Measure solutions of the steady Boltzmann equation in a slab. Comm. Math. Phys. 142, 285-296 (1991).
5. L. ARKERYD & N. MASLOVA, On diffuse reflection at the boundary for the Boltzmann equation and related equations. J. Stat. Phys., to appear.
6. L. ARKERYD & A. NOURI, Asymptotics of the Boltzmann equation with diffuse reflection boundary conditions. Preprint nr. 406, Département de Mathématiques, Université de Nice (1994).
7. M. BONY, Existence globale et diffusion en théorie cinétique discrète. In: Advances in Kinetic Theory and Continuum Mechanics. R. GATIGNOL & SOUBBARAMEYER, Eds., Springer-Verlag, Berlin (1991).
8. C. CERCIGNANI, Weak solutions of the Boltzmann equation and energy conservation. Appl. Math. Lett., 8, 53-59 (1995).
9. C. CERCIGNANI, A remarkable estimate for the solutions of the Boltzmann equation. Appl. Math. Lett. 5, 59-62 (1992).
10. C. CERCIGNANI, Theory and Application of the Boltzmann equation. Springer-Verlag, New York (1988).
11. C. CERCIGNANI, Equilibrium states and trend to equilibrium in a gas according to the Boltzmann equation. Rend. Mat. Appl. 10, 77-95 (1990).
12. C. CERCIGNANI, Errata: Weak solution of the Boltzmann equation and energy conservation. Appl. Math. Lett. 8, 95-99 (1995).
13. C. CERCIGNANI, R. ILLNER & M. PULVIRENTI, The Mathematical Theory of Dilute Gases. Springer-Verlag, New York (1994).
14. L. DESVILLETTES, Convergence to equilibrium in large time for Boltzmann and BGK equations. Arch. Rational Mech. Anal. 114, 47-55 (1991).
15. J. S. DARROZÈS & J. P. GUIRAUD, Généralisation formelle du théorème H en présence de parois. Applications. C.R.A.S. (Paris) A 262, 1368-1371 (1966).
16. R. DIPERNA & P. L. LIONS, On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Ann. Math. 130, 321-366 (1989).
17. P. L. LIONS, Compactness in Boltzmann's equation via Fourier integral operators and applications. I. Cahiers de Mathématiques de la décision no. 9301, CEREMADE (1993).
18. S. UKAI, Solutions of the Boltzmann equation. In: Patterns and waves - Qualitative analysis of nonlinear differential equations, 37-96 (1986).