Diffusive limit for finite velocity Boltzmann kinetic models

Revista Matematica Iberoamericana

Volumn 13, Issue 3, 1997, Pages 473-513

  Lions, Pierre Louis ^a   Toscani, Giuseppe ^b  

^a Centre National de la Recherche Scientifique   (France)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031315579     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/228     Document Type: Article

References (20)

1. Aronson, D. G., The porous media equations. In Non Linear Diffusion problems. Lecture Notes in Math. 1224, A. Fasano and M. Primicerio Eds., Springer Verlag, 1986.
2. Bardos, C., Golse, F., Perthame, B., Sentis, R., The nonaccretive radiative transfer equations: existence of solutions and Rosseland approximation. J. Funct. Anal. 77 (1988), 434-460.
3. Carleman, T., Problèmes Matematiques dans la Théorie Cinétique des Gaz. Almqvist-Wiksells, 1957.
4. Fitzgibbon, W. F., The fluid-dynamical limit of the Carleman equation with reflecting boundary. J. Nonlinear Anal. Theory Meth. Appl. 6 (1982), 695-702.
5. Fitzgibbon, W. F., Initial boundary value problem for the Carleman equation. Comput. Math. Appl. 9 (1983), 519-525.
6. Goldstein, S., On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. Appl. Math. 4 (1951), 129-156.
7. m when 0 < m < 1. Trans. Amer. Math. Soc. 291 (1985), 145-158.
8. Inoue, M., Derivation of a porous medium equation from many Markovian particles and the propagation of chaos. Hiroshima Math. J. 21 (1991), 85-110.
9. Kaper, H., Leaf, G. K., Reich, S., Convergence of semigroups with an application to the Carleman equation. Math. Meth. Appl. Sci. 2 (1980), 303-308.
10. Kurtz, T. G., Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics. Trans. Amer. Math. Soc. 186 (1973), 259-272.
11. Lions, J. L., Perturbations singulieres dans les problèmes aux limites et en controle optimale. Lecture Notes in Math. 323. Springer-Verlag, 1973.
12. Marcati, P., Milani, A. J., The one-dimensional darcy's law as the limit of a compressible euler flow. J. Differential Equations 84 (1990), 129-147.
13. McKean, H. P., The central limit theorem for Carleman's equation. Israel J. Math. 21 (1975), 54-92.
14. Murat, F., Compacitè par compensation. Ann. Scuola Norm. Sup. Pisa 5 (1978), 489-507.
15. Murat, F., Compacitè par compensation II. In Proceedings of the international Meeting on recent methods in Nonlinear Analysis, Roma, May 8-12 1978. E. DeGiorgi, E. Magenes and U. Mosco Eds. Pitagora Editrice, 1979, 245-256.
16. Oelschläger, K., Large systems of interacting particles and the porous medium equation. J. Differential Equations 88 (1990), 294-346.
17. Pulvirenti, A., Toscani, G., Fast diffusion as a limit of a two-velocity kinetic model. Rendiconti del Circolo Matematico di Palermo 45 (1996), 417-426.
18. Tartar, L., Homogénéisation et compacité par compensation. Séminaire Goulaouic-Schwartz 1978-79. Ecole Politechnique, Palaiseau (1979) Exposé n. 9.
19. Tartar, L., Compensated compactness and applications to partial differential equations. In Non-linear Analysis and Mechanics, Heriot-Watt Symposium, Vol. IV. Ed. by R.J. Knops. Research Notes in Math. 39, Pitman, 1979, 136-212.
20. Taylor, G. I., Diffusion by continuous movements. Proc. London Math. Soc. 20 (1921), 196-212.