The diffusive limit for Carleman-type kinetic models

Nonlinearity

Volumn 18, Issue 3, 2005, Pages 1223-1248

  Salvarani, Francesco ^a   Vázquez, Juan Luis ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29744466708     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/3/015     Document Type: Article

References (21)

1. Bénilan P 1972 Equations d'évolution dans un espace de Banach quelconque et applications PhD Thesis University of Orsay (in French)
2. 1, - Δφ)(u) = 0 Indiana Univ. Math. J. 30 161-77
3. Carleman T 1957 Problèmes mathématiques dans la théorie cinétique des gaz (Uppsala: Almqvist-Wiksells)
4. Crandall M G and Liggett T M 1971 Generation of semi-groups of nonlinear transformations on general Banach spaces Am. J. Math. 93 265-98
5. Donatelli D and Marcati P 2004 Convergence of singular limits for multi-D semilinear hyperbolic systems to parabolic systems Trans. Am. Math. Soc. 356 2093-121
6. Esteban J R, Rodriguez A and Vázquez J L 1988 A nonlinear heat equation with singular diffusivity Commun. Partial Diff. Eqns 13 985-1039
7. Fitzgibbon W E 1982 The fluid-dynamical limit of the Carleman equation with reflecting boundary J. Nonlinear Anal. Theory Methods Appl. 6 695-702
8. Ito K and Kappel F 2002 Evolution Equations and Approximations (Singapore: World Scientific)
9. Kurtz T G 1973 Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics Trans. Am. Math. Soc. 186 259-72
10. Ladyženskaja O A, Solonnikov V A and Ural'ceva N N 1967 Linear and Quasilinear Equations of Parabolic Type (Translations of Mathematical Monographs vol 23) (Providence, RI: American Mathematical Society)
11. Lions P L and Toscani G 1997 Diffusive limits for finite velocities Boltzmann kinetic models Rev. Mat. Iberoamericana 13 473-513
12. Marcati P and Rubino B 2000 Hyperbolic to parabolic relaxation theory for quasilinear first order systems J. Diff. Eqns 162 359-99
13. McKean H P 1975 The central limit theorem for Carleman's equation Israel J. Math. 21 54-92
14. Murat F 1978 Compacité par compensation Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 489-507
15. 1, - Δφ(u) = 0 with initial datum a measure Nonlinear Anal. TMA 6 175-87
16. Płatkowski T and Diner R1988 Discrete velocity models of the Boltzmann equation: a survey on the mathematical aspects of the theory SIAM Rev. 30 213-55
17. Pulvirenti A and Toscani G 1996 Fast diffusion as a limit of a two-velocity kinetic model Rend. Circ. Mat. Palermo Suppl. 45 521-8
18. Rodríguez A and Vázquez J L 1990 A well posed problem in singular Fickian diffusion Arch. Ration. Mech. Anal. 110 141-63
19. Rodríguez A and Vázquez J L 1995 Nonuniqueness of solutions of nonlinear heat equations of fast diffusion type Ann. Inst. H Poincaré, Anal. Non Linéaire 12 173-200
20. Salvarani F 1999 Diffusion limits for the initial-boundary value problem of the Goldstein-Taylor model Rend. Sem. Mat. Univ. Politec. Torino 57 209-20
21. Vázquez J L 1992 Nonexistence of solutions for nonlinear heat equations of fast-diffusion type J. Math. Pure Appl. 71 503-26