메뉴 건너뛰기




Volumn 41, Issue 2, 2004, Pages 205-244

Mathematical tools for kinetic equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 2142694481     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-04-01004-3     Document Type: Article
Times cited : (91)

References (120)
  • 1
    • 0000186090 scopus 로고
    • Spaces of functions with differential-difference characteristics and smoothness of solutions of the transport equation
    • MR 86a:46033
    • Agoshkov, V. I. Spaces of functions with differential-difference characteristics and smoothness of solutions of the transport equation. Soviet Math. Dokl. 29 (1984), 662-666. MR 86a:46033
    • (1984) Soviet Math. Dokl. , vol.29 , pp. 662-666
    • Agoshkov, V.I.1
  • 3
    • 0033469593 scopus 로고    scopus 로고
    • Homogenization of the criticality spectral equation in neutron transport
    • MR 2001c:35025
    • Allaire, G.; Bal, G. Homogenization of the criticality spectral equation in neutron transport. M2AN Math. Model. Numer. Anal. 33 (1999), no. 4, 721-746. MR 2001c:35025
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.4 , pp. 721-746
    • Allaire, G.1    Bal, G.2
  • 4
    • 0001288465 scopus 로고
    • 1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation
    • MR 91m:82114
    • 1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation. J. Statist, Phys. 59 (1990), no. 3-4, 845-867. MR 91m:82114
    • (1990) J. Statist, Phys. , vol.59 , Issue.3-4 , pp. 845-867
    • Arkeryd, L.1    Cercignani, C.2
  • 5
    • 0042241164 scopus 로고    scopus 로고
    • 1 solutions to the stationary Boltzmann equation in a slab
    • MR 2002d:82061
    • 1 solutions to the stationary Boltzmann equation in a slab. Ann. Fac. Sci. Toulouse Math. (6) 9 (2000), no. 3, 375-413. MR 2002d:82061
    • (2000) Ann. Fac. Sci. Toulouse Math. (6) , vol.9 , Issue.3 , pp. 375-413
    • Arkeryd, L.1    Nouri, A.2
  • 6
    • 0035621902 scopus 로고    scopus 로고
    • Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems
    • The Sixteenth International Conference on Transport Theory, Part I (Atlanta, GA, 1999). MR 2002h:82080
    • Arnold, A.; Carrillo, J. A.; Gamba, I. M.; Shu, C.-W. Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems. The Sixteenth International Conference on Transport Theory, Part I (Atlanta, GA, 1999). Transport Theory Statist. Phys. 30 (2001), no. 2-3, 121-153. MR 2002h:82080
    • (2001) Transport Theory Statist. Phys. , vol.30 , Issue.2-3 , pp. 121-153
    • Arnold, A.1    Carrillo, J.A.2    Gamba, I.M.3    Shu, C.-W.4
  • 7
    • 84974746772 scopus 로고
    • Diffusion approximation for a Knudsen gas in a thin domain with accommodation on the boundary
    • MR 91m:76095
    • Babovsky, H.; Bardos, C.; Platkowski, T. Diffusion approximation for a Knudsen gas in a thin domain with accommodation on the boundary. Asymptotic Anal. 3 (1991), no. 4, 265-289. MR 91m:76095
    • (1991) Asymptotic Anal. , vol.3 , Issue.4 , pp. 265-289
    • Babovsky, H.1    Bardos, C.2    Platkowski, T.3
  • 8
    • 65449177851 scopus 로고
    • Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
    • MR 86k:35129
    • Bardos, C.; Degond, P. Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 2, 101-118. MR 86k:35129
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , Issue.2 , pp. 101-118
    • Bardos, C.1    Degond, P.2
  • 9
    • 84990619144 scopus 로고
    • Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation
    • MR 94g:82039
    • Bardos, C.; Golse, F.; Levermore, C. D. Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Comm. Pure Appl. Math. 46 (1993), no. 5, 667-753. MR 94g:82039
    • (1993) Comm. Pure Appl. Math. , vol.46 , Issue.5 , pp. 667-753
    • Bardos, C.1    Golse, F.2    Levermore, C.D.3
  • 10
    • 50849147116 scopus 로고
    • The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximation
    • MR 89f:35174
    • Bardos, C.; Golse, F.; Perthame, B.; Sentis, R. The nonaccretive radiative transfer equations: existence of solutions and Rosseland approximation, J. Funct. Anal. 77 (1988), no. 2, 434-460. MR 89f:35174
    • (1988) J. Funct. Anal. , vol.77 , Issue.2 , pp. 434-460
    • Bardos, C.1    Golse, F.2    Perthame, B.3    Sentis, R.4
  • 11
    • 84967735805 scopus 로고
    • Diffusion approximation and computation of the critical size
    • MR 86g:45027
    • Bardos, C.; Santos, R.; Sentis, R. Diffusion approximation and computation of the critical size. Trans. Amer. Math. Soc. 284 (1984), no. 2, 617-649. MR 86g:45027
    • (1984) Trans. Amer. Math. Soc. , vol.284 , Issue.2 , pp. 617-649
    • Bardos, C.1    Santos, R.2    Sentis, R.3
  • 12
    • 0000141020 scopus 로고
    • Global classical solutions of the periodic Vlasov-Poisson system in three dimensions
    • MR 92f:35138
    • Batt, J.; Rein, G. Global classical solutions of the periodic Vlasov-Poisson system in three dimensions. C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 6, 411-416. MR 92f:35138
    • (1991) C. R. Acad. Sci. Paris Sér. I Math. , vol.313 , Issue.6 , pp. 411-416
    • Batt, J.1    Rein, G.2
  • 13
    • 0001103153 scopus 로고
    • A rigorous stability result for the Vlasov-Poisson system in three dimensions
    • MR 95a:82106
    • Batt, J.; Rein, G. A rigorous stability result for the Vlasov-Poisson system in three dimensions. Ann. Mat. Pura Appl. (4) 164 (1993), 133-154. MR 95a:82106
    • (1993) Ann. Mat. Pura Appl. (4) , vol.164 , pp. 133-154
    • Batt, J.1    Rein, G.2
  • 14
    • 0034254401 scopus 로고    scopus 로고
    • Modeling and mathematical problems related to tumors immune system interactions
    • MR 2001i:92016
    • Bellomo, N; Preziosi, L. Modeling and mathematical problems related to tumors immune system interactions. Comp. Modelling 32 (2000), 413-452. MR 2001i:92016
    • (2000) Comp. Modelling , vol.32 , pp. 413-452
    • Bellomo, N.1    Preziosi, L.2
  • 16
    • 0013257426 scopus 로고
    • The Child-Langmuir law in the kinetic theory of charged particles: Semiconductors models
    • Mathematical Problems in Semiconductor Physics (Rome), Longman, Harlow, 1995. MR 98j:82074
    • Ben Abdallah, N.; Degond, P. The Child-Langmuir law in the kinetic theory of charged particles: semiconductors models. Mathematical problems in semiconductor physics (Rome, 1993), 76-102, Pitman Res. Notes Math. Ser., 340, Longman, Harlow, 1995. MR 98j:82074
    • (1993) Pitman Res. Notes Math. Ser. , pp. 76-102
    • Ben Abdallah, N.1    Degond, P.2
  • 18
    • 0033204043 scopus 로고    scopus 로고
    • A hydrodynamic model arising in the context of granular media
    • MR 2000g:76092
    • Benedetto, D.; Caglioti, E.; Golse, F.; Pulvirenti, M. A hydrodynamic model arising in the context of granular media. Comput. Math. Appl. 38 (1999), no. 7-8, 121-131. MR 2000g:76092
    • (1999) Comput. Math. Appl. , vol.38 , Issue.7-8 , pp. 121-131
    • Benedetto, D.1    Caglioti, E.2    Golse, F.3    Pulvirenti, M.4
  • 19
    • 0035643773 scopus 로고    scopus 로고
    • On the one-dimensional Boltzmann equation for granular flows
    • MR 2002h:82066
    • Benedetto, D.; Pulvirenti, M. On the one-dimensional Boltzmann equation for granular flows, M2AN Math. Model. Numer. Anal. 35 (2001), no. 5, 899-905. MR 2002h:82066
    • (2001) M2AN Math. Model. Numer. Anal. , vol.35 , Issue.5 , pp. 899-905
    • Benedetto, D.1    Pulvirenti, M.2
  • 21
    • 0002665670 scopus 로고
    • Régularité précisée des moyennes dans les équations de transport
    • MR 95g:82083
    • Bézard, M. Régularité précisée des moyennes dans les équations de transport. Bull. Soc. Math. France 122 (1994), 29-76. MR 95g:82083
    • (1994) Bull. Soc. Math. France , vol.122 , pp. 29-76
    • Bézard, M.1
  • 22
    • 0034343060 scopus 로고    scopus 로고
    • On some properties of kinetic and hydrodynamic equations for inelastic interactions
    • MR 2001c:82063
    • Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M. On some properties of kinetic and hydrodynamic equations for inelastic interactions. J. Statist. Phys. 98 (2000), no. 3-4, 743-773. MR 2001c:82063
    • (2000) J. Statist. Phys. , vol.98 , Issue.3-4 , pp. 743-773
    • Bobylev, A.V.1    Carrillo, J.A.2    Gamba, I.M.3
  • 23
    • 0001686361 scopus 로고
    • Smoothing effect for the non-linear Vlasov-Poisson-Fokker-Planck system
    • MR 06g:35198
    • Bouchut, F.; Smoothing effect for the non-linear Vlasov-Poisson-Fokker- Planck system. J. Differential Equations 122 (1995), no. 2, 225-238. MR 06g:35198
    • (1995) J. Differential Equations , vol.122 , Issue.2 , pp. 225-238
    • Bouchut, F.1
  • 24
    • 22644449510 scopus 로고    scopus 로고
    • Averaging lemmas without time Fourier transform and application to discretized kinetic equations
    • MR 2000b:82024
    • Bouchut, F.; Desvillettes, L. Averaging lemmas without time Fourier transform and application to discretized kinetic equations. Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), no. 1, 19-36. MR 2000b:82024
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , Issue.1 , pp. 19-36
    • Bouchut, F.1    Desvillettes, L.2
  • 25
    • 84972497473 scopus 로고
    • On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
    • MR 051:82076
    • Bouchut, F.; Dolbeault, J. On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials. Differential Integral Equations 8 (1995), no. 3, 487-514. MR 051:82076
    • (1995) Differential Integral Equations , vol.8 , Issue.3 , pp. 487-514
    • Bouchut, F.1    Dolbeault, J.2
  • 26
    • 0009886850 scopus 로고    scopus 로고
    • Kinetic Equations and Asymptotic Theories
    • L. Desvillettes and B. Perthame ed., Elsevier
    • Bouchut, F.; Golse, F.; Pulvirenti, M. in Kinetic Equations and Asymptotic Theories, L. Desvillettes and B. Perthame ed., Series in Appl. Math. no. 4, Elsevier (2000).
    • (2000) Series in Appl. Math. , Issue.4
    • Bouchut, F.1    Golse, F.2    Pulvirenti, M.3
  • 27
    • 0012113742 scopus 로고    scopus 로고
    • Averages over spheres for kinetic transport equations; Hyperbolic Sobolev spaces and Strichartz inequalities
    • MR 2002b:82051
    • Bournaveas, N.; Perthame, B. Averages over spheres for kinetic transport equations; hyperbolic Sobolev spaces and Strichartz inequalities. J. Math. Pures Appl. (9) 80 (2001), no. 5, 517-534. MR 2002b:82051
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.5 , pp. 517-534
    • Bournaveas, N.1    Perthame, B.2
  • 28
    • 0000373558 scopus 로고    scopus 로고
    • Convergence of the Vlasov-Poisson system to the incompressible Euler equations
    • MR 2001c:76124
    • Brenier, Y. Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations 25 (2000), no. 3-4, 737-754. MR 2001c:76124
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.3-4 , pp. 737-754
    • Brenier, Y.1
  • 29
    • 84980175331 scopus 로고
    • The fluid dynamic limit of the nonlinear Boltzmann equation
    • MR 81j:76072
    • Caflisch, R. E. The fluid dynamic limit of the nonlinear Boltzmann equation. Comm. Pure Appl. Math. 33 (1980), no. 5, 651-666. MR 81j:76072
    • (1980) Comm. Pure Appl. Math. , vol.33 , Issue.5 , pp. 651-666
    • Caflisch, R.E.1
  • 30
    • 0036384820 scopus 로고    scopus 로고
    • On the two-dimensional Vlasov-Helmholtz equation with infinite
    • MR 2003b:82056
    • Caprino, S.; Marchions, C.; Pulvirenti, M. On the two-dimensional Vlasov-Helmholtz equation with infinite mass. Comm. Partial Differential Equations 27 (2002), no. 3-4, 791-808. MR 2003b:82056
    • (2002) Mass. Comm. Partial Differential Equations , vol.27 , Issue.3-4 , pp. 791-808
    • Caprino, S.1    Marchions, C.2    Pulvirenti, M.3
  • 31
    • 0010306013 scopus 로고    scopus 로고
    • Strichartz estimates for kinetic transport equations
    • MR 98f:35133
    • Castella, F.; Perthame, B. Strichartz estimates for kinetic transport equations. C. R. Acad. Sc. Série I Math. 322, no. 6 (1996), 535-540. MR 98f:35133
    • (1996) C. R. Acad. Sc. Série I Math. , vol.322 , Issue.6 , pp. 535-540
    • Castella, F.1    Perthame, B.2
  • 32
    • 0003287218 scopus 로고
    • The Boltzmann equation and its application
    • Springer-Verlag, Berlin. MR 961:82082
    • Cercignani, C.; The Boltzmann equation and its application. Applied Math. Sciences 67, Springer-Verlag, Berlin (1988). MR 961:82082
    • (1988) Applied Math. Sciences , vol.67
    • Cercignani, C.1
  • 33
    • 0003200990 scopus 로고
    • The mathematical theory of dilute gases
    • Springer-Verlag, Berlin. MR 96g:82046
    • Cercignani, C.; Illner, R.; Pulvirenti, M. The mathematical theory of dilute gases. Applied Math. Sciences 106, Springer-Verlag, Berlin (1994). MR 96g:82046
    • (1994) Applied Math. Sciences , vol.106
    • Cercignani, C.1    Illner, R.2    Pulvirenti, M.3
  • 35
    • 0348125356 scopus 로고    scopus 로고
    • Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
    • Chen, G.-Q.; Perthame, B. Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 4, 645-668.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.4 , pp. 645-668
    • Chen, G.-Q.1    Perthame, B.2
  • 37
    • 0004189342 scopus 로고    scopus 로고
    • Modeling of collisions
    • With contributions by I. Gasser, A. Unterreiter and L. Desvillettes. Edited and with a foreword by P. A. Raviart. Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris; North-Holland, Amsterdam. MR 2000b:76092
    • Decoster, A.; Markowich, P. A.; Perthame, B. Modeling of collisions. With contributions by I. Gasser, A. Unterreiter and L. Desvillettes. Edited and with a foreword by P. A. Raviart. Series in Applied Mathematics, 2. Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris; North-Holland, Amsterdam, 1998. MR 2000b:76092
    • (1998) Series in Applied Mathematics , vol.2
    • Decoster, A.1    Markowich, P.A.2    Perthame, B.3
  • 38
    • 0002624297 scopus 로고    scopus 로고
    • Mathematical modelling of microelectronics semiconductor devices
    • Some current topics on nonlinear conservation laws, AMS/IP, Amer. Math. Soc., Providence, RI. MR 2001h:82108
    • Degond, P. Mathematical modelling of microelectronics semiconductor devices. Some current topics on nonlinear conservation laws, 77-110, AMS/IP Stud. Adv. Math., 15, Amer. Math. Soc., Providence, RI (2000). MR 2001h:82108
    • (2000) Stud. Adv. Math. , vol.15 , pp. 77-110
    • Degond, P.1
  • 39
    • 0000512903 scopus 로고    scopus 로고
    • Diffusion limit for nonhomogeneous and non-micro-reversible processes
    • MR 2002a:35012
    • Degond, P.; Goudon, T.; Poupaud, F. Diffusion limit for nonhomogeneous and non-micro-reversible processes. Indiana Univ. Math. J. 49 (2000), no. 3, 1175-1198. MR 2002a:35012
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.3 , pp. 1175-1198
    • Degond, P.1    Goudon, T.2    Poupaud, F.3
  • 40
    • 0035541515 scopus 로고    scopus 로고
    • High-field approximations of the energy-transport model for semiconductors with non-parabolic band structure
    • MR 2002j:82120
    • Degond, P.; Jüngel, A. High-field approximations of the energy-transport model for semiconductors with non-parabolic band structure. Z. Angew. Math. Phys. 52 (2001), no. 6, 1053-1070. MR 2002j:82120
    • (2001) Z. Angew. Math. Phys. , vol.52 , Issue.6 , pp. 1053-1070
    • Degond, P.1    Jüngel, A.2
  • 41
    • 0000583046 scopus 로고
    • The Fokker-Plansk asymptotics of the Boltzmann collision operator in the Coulomb case
    • MR 93g:82083
    • Degond, P.; Lucquin-Desreux, B. The Fokker-Plansk asymptotics of the Boltzmann collision operator in the Coulomb case. Math. Mod. Meth. Appl. Sc. 2 (1992), no. 2, 167-182. MR 93g:82083
    • (1992) Math. Mod. Meth. Appl. Sc. , vol.2 , Issue.2 , pp. 167-182
    • Degond, P.1    Lucquin-Desreux, B.2
  • 42
    • 0000195197 scopus 로고
    • On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
    • MR 92b:35153
    • Desvillettes, L.; Dolbeault, J. On long time asymptotics of the Vlasov-Poisson-Boltzmann equation. Comm. Partial Differential Equations 16 (1991), no. 2-3, 451-489. MR 92b:35153
    • (1991) Comm. Partial Differential Equations , vol.16 , Issue.2-3 , pp. 451-489
    • Desvillettes, L.1    Dolbeault, J.2
  • 43
    • 0035526707 scopus 로고    scopus 로고
    • On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation
    • MR 2001h:82079
    • Desvillettes, L.; Villani, C. On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: the linear Fokker-Planck equation. Comm. Pure Appl. Math. 54 (2001), no. 1, 1-42. MR 2001h:82079
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.1 , pp. 1-42
    • Desvillettes, L.1    Villani, C.2
  • 45
    • 0035586098 scopus 로고    scopus 로고
    • The averaging lemma
    • (electronic). MR 2002b:35130
    • DeVore R.; Petrova G. P. The averaging lemma, J. Amer, Math. Soc. 14 (2001), no. 2, 279-296 (electronic). MR 2002b:35130
    • (2001) J. Amer, Math. Soc. , vol.14 , Issue.2 , pp. 279-296
    • DeVore, R.1    Petrova, G.P.2
  • 46
    • 0000445095 scopus 로고
    • Solutions globales d'équations du type Vlasov-Poisson
    • French. MR 89k:35202
    • DiPerna, R.; Lions, P.-L. Solutions globales d'équations du type Vlasov-Poisson. (French) [Global solutions of Vlasov-Poisson type equations] C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 12, 655-658. MR 89k:35202
    • (1988) C. R. Acad. Sci. Paris Sér. I Math. , vol.307 , Issue.12 , pp. 655-658
    • Diperna, R.1    Lions, P.-L.2
  • 47
    • 84990553444 scopus 로고
    • Global weak solutions of Vlasov-Maxwell systems
    • MR 90i:35236
    • DiPerna, R. J.; Lions, P.-L. Global weak solutions of Vlasov-Maxwell systems. Comm. Pure Appl. Math. 42 (1989), no. 6, 729-757. MR 90i:35236
    • (1989) Comm. Pure Appl. Math. , vol.42 , Issue.6 , pp. 729-757
    • Diperna, R.J.1    Lions, P.-L.2
  • 48
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • MR 90j:34004
    • DiPerna, R. J.; Lions, P.-L. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989), no. 3, 511-547. MR 90j:34004
    • (1989) Invent. Math. , vol.98 , Issue.3 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.-L.2
  • 49
    • 0001089576 scopus 로고
    • On the Cauchy problem for the Boltzmann equation: Global existence and weak stability results
    • MR 90k:82045
    • DiPerna, R. J.; Lions, P.-L. On the Cauchy problem for the Boltzmann equation: global existence and weak stability results. Annals of Math 130 (1989), 321-366. MR 90k:82045
    • (1989) Annals of Math , vol.130 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.-L.2
  • 51
    • 0033074708 scopus 로고    scopus 로고
    • Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: External potential and confinement
    • large time behavior and steady states. MR 99m:35248
    • Dolbeault, J. Free energy and solutions of the Vlasov-Poisson-Fokker- Planck system: external potential and confinement (large time behavior and steady states). J. Math. Pures Appl. (9) 78 (1999), no. 2, 121-157. MR 99m:35248
    • (1999) J. Math. Pures Appl. (9) , vol.78 , Issue.2 , pp. 121-157
    • Dolbeault, J.1
  • 52
    • 0033570799 scopus 로고    scopus 로고
    • Etude théorique et numérique d'une hiérarchie de modèles aux moments pour le transfert radiatif
    • French. MR 2000h:85005
    • Dubroca, B.; Feugeas, J.-L. Etude théorique et numérique d'une hiérarchie de modèles aux moments pour le transfert radiatif. (French) [Theoretical and numerical study of a moment closure hierarchy for the radiative transfer equation] C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 10, 915-920. MR 2000h:85005
    • (1999) C. R. Acad. Sci. Paris Sér. I Math. , vol.329 , Issue.10 , pp. 915-920
    • Dubroca, B.1    Feugeas, J.-L.2
  • 53
    • 0037908268 scopus 로고    scopus 로고
    • On a quantum Boltzmann equation for a gas of photons
    • MR 2002j:82071
    • Escobedo, M.; Mischler, S. On a quantum Boltzmann equation for a gas of photons. J. Math. Pures Appl. (9) 80 (2001), no. 5, 471-515. MR 2002j:82071
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.5 , pp. 471-515
    • Escobedo, M.1    Mischler, S.2
  • 55
    • 0035541154 scopus 로고    scopus 로고
    • The finite Larmor radius approximation
    • electronic. MR 2002g:82049
    • Frénod, E.; Sonnendrücker, E. The finite Larmor radius approximation. SIAM J. Math. Anal. 32 (2001), no. 6, 1227-1247 (electronic). MR 2002g:82049
    • (2001) SIAM J. Math. Anal. , vol.32 , Issue.6 , pp. 1227-1247
    • Frénod, E.1    Sonnendrücker, E.2
  • 56
    • 23044522112 scopus 로고    scopus 로고
    • Regularity and propagation of moments in some nonlinear Vlasov systems
    • MR 2001J:82101
    • Gasser, I.; Jabin, P.-E.; Perthame, B. Regularity and propagation of moments in some nonlinear Vlasov systems. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), no. 6, 1259-1273. MR 2001J:82101
    • (2000) Proc. Roy. Soc. Edinburgh Sect. A , vol.130 , Issue.6 , pp. 1259-1273
    • Gasser, I.1    Jabin, P.-E.2    Perthame, B.3
  • 57
    • 0003090940 scopus 로고
    • Moyennisation et régularité deux-microlocale
    • French. MR 91g:35068
    • Gérard, P. Moyennisation et régularité deux-microlocale. (French) [Second-microlocal averaging and regularity]. Ann. Sci. École Norm. Sup. (4) 23 (1990), no. 1, 89-121. MR 91g:35068
    • (1990) Ann. Sci. École Norm. Sup. (4) , vol.23 , Issue.1 , pp. 89-121
    • Gérard, P.1
  • 58
    • 84990553452 scopus 로고
    • Averaging regularity results for PDEs under transversality assumptions
    • MR 92k:35044
    • Gérard, P.; Golse, F. Averaging regularity results for PDEs under transversality assumptions. Comm. Pure Appl. Math. 45 (1992), no. 1, 1-26. MR 92k:35044
    • (1992) Comm. Pure Appl. Math. , vol.45 , Issue.1 , pp. 1-26
    • Gérard, P.1    Golse, F.2
  • 60
    • 85050669204 scopus 로고
    • The global Cauchy problem for some nonlinear Schrödinger equation revisited
    • MR 87b:35150
    • Ginibre, J.; Velo, G. The global Cauchy problem for some nonlinear Schrödinger equation revisited, Ann. Inst. H. Poincaré, Analyse non linéaire 2 (1985) 309-327. MR 87b:35150
    • (1985) Ann. Inst. H. Poincaré, Analyse Non Linéaire , vol.2 , pp. 309-327
    • Ginibre, J.1    Velo, G.2
  • 62
    • 85043347731 scopus 로고    scopus 로고
    • The relativistic Vlasov-Maxwell system in 2D and 2.5D. Nonlinear wave equations
    • Providence, RI, Amer. Math. Soc., Providence, RI, 2000. MR 2001f:35247
    • Glassey, R. T.; Schaeffer, J. The relativistic Vlasov-Maxwell system in 2D and 2.5D. Nonlinear wave equations (Providence, RI, 1998), 61-69, Contemp. Math., 263, Amer. Math. Soc., Providence, RI, 2000. MR 2001f:35247
    • (1998) Contemp. Math. , vol.263 , pp. 61-69
    • Glassey, R.T.1    Schaeffer, J.2
  • 63
    • 21844481340 scopus 로고
    • Asymptotic stability of the relativistic Maxwellian via fourteen moments
    • MR 96c:82054
    • Glassey, R. T.; Strauss, W. A. Asymptotic stability of the relativistic Maxwellian via fourteen moments. Transport Theory Statist. Phys. 24 (1995), no. 4-5, 657-678. MR 96c:82054
    • (1995) Transport Theory Statist. Phys. , vol.24 , Issue.4-5 , pp. 657-678
    • Glassey, R.T.1    Strauss, W.A.2
  • 64
    • 0033244167 scopus 로고    scopus 로고
    • Decay of the linearized Boltzmann-Vlasov system
    • MR 2000c:35238
    • Glassey, R. T.; Strauss, W. A. Decay of the linearized Boltzmann-Vlasov system. Transport Theory Statist. Phys. 28 (1999), no. 2, 135-156. MR 2000c:35238
    • (1999) Transport Theory Statist. Phys. , vol.28 , Issue.2 , pp. 135-156
    • Glassey, R.T.1    Strauss, W.A.2
  • 65
    • 45549114712 scopus 로고
    • Regularity of the moments of the solution of a transport equation
    • MR 89a:35179
    • Golse, F.; Lions, P.-L.; Perthame, B.; Sentis, R. Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76 (1988) 110-125. MR 89a:35179
    • (1988) J. Funct. Anal. , vol.76 , pp. 110-125
    • Golse, F.1    Lions, P.-L.2    Perthame, B.3    Sentis, R.4
  • 66
    • 0000053323 scopus 로고
    • Un résultat de compacité pour les équations du transport
    • MR 88m:82062
    • Golse, F.; Perthame, B.; Sentis, R. Un résultat de compacité pour les équations du transport. . ., C. R. Acad. Sci. Paris, Série I Math. 301 (1985) 341-344. MR 88m:82062
    • (1985) C. R. Acad. Sci. Paris, Série I Math. , vol.301 , pp. 341-344
    • Golse, F.1    Perthame, B.2    Sentis, R.3
  • 67
    • 0033209561 scopus 로고    scopus 로고
    • The Vlasov-Poisson system with strong magnetic field
    • MR 2000g:35209
    • Golse, F.; Saint-Raymond, L. The Vlasov-Poisson system with strong magnetic field. J. Math. Pures Appl. (9) 78 (1999), no. 8, 791-817. MR 2000g:35209
    • (1999) J. Math. Pures Appl. (9) , vol.78 , Issue.8 , pp. 791-817
    • Golse, F.1    Saint-Raymond, L.2
  • 68
    • 0742323595 scopus 로고    scopus 로고
    • The Navier-Stokes limit of Boltzmann equation: Convergence proof
    • Golse, F.; Saint-Raymond, L. The Navier-Stokes limit of Boltzmann equation: convergence proof. Inventiones Mathematicae 155, no. 1 (2004), 81-161.
    • (2004) Inventiones Mathematicae , vol.155 , Issue.1 , pp. 81-161
    • Golse, F.1    Saint-Raymond, L.2
  • 70
    • 0000454055 scopus 로고    scopus 로고
    • Approximation by homogenization and diffusion of kinetic equations
    • MR 2002e:35195
    • Goudon, T.; Poupaud, F. Approximation by homogenization and diffusion of kinetic equations. Comm. Partial Differential Equations 26 (2001), no. 3-4, 537-569. MR 2002e:35195
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.3-4 , pp. 537-569
    • Goudon, T.1    Poupaud, F.2
  • 71
    • 0005604229 scopus 로고    scopus 로고
    • Oscillations in quasineutral plasmas
    • MR 98g:82033
    • Grenier, E. Oscillations in quasineutral plasmas. Comm. Partial Differential Equations 21 (1996), no. 3-4, 363-394. MR 98g:82033
    • (1996) Comm. Partial Differential Equations , vol.21 , Issue.3-4 , pp. 363-394
    • Grenier, E.1
  • 72
    • 0032474668 scopus 로고    scopus 로고
    • Unstable BGK solitary waves and collisionless shocks
    • MR 2000k:35239b
    • Guo, Y.; Strauss, W. A. Unstable BGK solitary waves and collisionless shocks. Comm. Math. Phys. 195 (1998), no. 2, 267-293. MR 2000k:35239b
    • (1998) Comm. Math. Phys. , vol.195 , Issue.2 , pp. 267-293
    • Guo, Y.1    Strauss, W.A.2
  • 73
    • 0034363471 scopus 로고    scopus 로고
    • Magnetically created instability in a collisionless plasma
    • MR 2001k:76053
    • Guo, Y.; Strauss, W. A. Magnetically created instability in a collisionless plasma. J. Math. Pures Appl. (9) 79 (2000), no. 10, 975-1009. MR 2001k:76053
    • (2000) J. Math. Pures Appl. (9) , vol.79 , Issue.10 , pp. 975-1009
    • Guo, Y.1    Strauss, W.A.2
  • 74
    • 0042947432 scopus 로고    scopus 로고
    • Global existence and large time behaviour of solutions for Vlasov-Stokes equations
    • MR 99f:76128
    • Hamdache, K. Global existence and large time behaviour of solutions for Vlasov-Stokes equations. Japan J. Indust. Appl. Math. 15 (1998), 51-74. MR 99f:76128
    • (1998) Japan J. Indust. Appl. Math. , vol.15 , pp. 51-74
    • Hamdache, K.1
  • 75
    • 0019655802 scopus 로고
    • On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation
    • Horst, E. On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I. Math. Meth. Appl. Sci. 3 (1981), 229-248; and II. Math. Meth. Appl. Sci. 4 (1982), 19-32. MR 83h:35110, MR 84b:85001
    • (1981) I. Math. Meth. Appl. Sci. , vol.3 , pp. 229-248
    • Horst, E.1
  • 76
    • 0019655802 scopus 로고
    • MR 83h:35110, MR 84b:85001
    • Horst, E. On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I. Math. Meth. Appl. Sci. 3 (1981), 229-248; and II. Math. Meth. Appl. Sci. 4 (1982), 19-32. MR 83h:35110, MR 84b:85001
    • (1982) II. Math. Meth. Appl. Sci. , vol.4 , pp. 19-32
  • 77
    • 0021303282 scopus 로고
    • Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation
    • MR 85j:45026
    • Horst, E.; Hunze, R. Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation. Math. Methods Appl. Sci. 6 (1984), no. 2, 262-279. MR 85j:45026
    • (1984) Math. Methods Appl. Sci. , vol.6 , Issue.2 , pp. 262-279
    • Horst, E.1    Hunze, R.2
  • 78
    • 0000416212 scopus 로고    scopus 로고
    • A kinetic model for vehicular traffic: Existence of stationary solutions
    • MR 2000e:90010
    • Illner, R.; Klar, A.; Lange, H.; Unterreiter, A.; Wegener, R. A kinetic model for vehicular traffic: existence of stationary solutions. J. Math. Anal. Appl. 237 (1999) no. 2, 622-643. MR 2000e:90010
    • (1999) J. Math. Anal. Appl. , vol.237 , Issue.2 , pp. 622-643
    • Illner, R.1    Klar, A.2    Lange, H.3    Unterreiter, A.4    Wegener, R.5
  • 79
    • 0030285853 scopus 로고    scopus 로고
    • Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case
    • MR 97j:35153
    • Illner, R.; Rein, G. Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case. Math. Methods Appl. Sci. 19 (1996), no. 17, 1409-1413. MR 97j:35153
    • (1996) Math. Methods Appl. Sci. , vol.19 , Issue.17 , pp. 1409-1413
    • Illner, R.1    Rein, G.2
  • 80
    • 0005525756 scopus 로고    scopus 로고
    • Macroscopic limit of Vlasov type equations with friction
    • MR 2002i:82079
    • Jabin, P.-E. Macroscopic limit of Vlasov type equations with friction. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000), no. 5, 651-672. MR 2002i:82079
    • (2000) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.17 , Issue.5 , pp. 651-672
    • Jabin, P.-E.1
  • 81
    • 0002638915 scopus 로고    scopus 로고
    • Notes on mathematical problems on the dynamics of dispersed particles interacting through a fluid
    • N. Bellomo and M. Pulvirenti editors, Birkhäuser, Boston. MR 2002b:76098
    • Jabin, P.-E.; Perthame, B. Notes on mathematical problems on the dynamics of dispersed particles interacting through a fluid. In N. Bellomo and M. Pulvirenti editors, Modelling in applied sciences, a kinetic theory approach, Birkhäuser, Boston (2000). MR 2002b:76098
    • (2000) Modelling in Applied Sciences, a Kinetic Theory Approach
    • Jabin, P.-E.1    Perthame, B.2
  • 82
    • 0142065370 scopus 로고    scopus 로고
    • Regularity in kinetic formulations via averaging lemmas. ESAIM:COCV special issue in memory of J.-L. Lions (2002)
    • electronic. MR 2003j:35207
    • Jabin, P.-E.; Perthame, B. Regularity in kinetic formulations via averaging lemmas. ESAIM:COCV special issue in memory of J.-L. Lions (2002), ESAIM Control Optim. Gale. Var. 8 (2002), 761-774 (electronic). MR 2003j:35207
    • (2002) ESAIM Control Optim. Gale. Var. , vol.8 , pp. 761-774
    • Jabin, P.-E.1    Perthame, B.2
  • 84
    • 0032259525 scopus 로고    scopus 로고
    • Domain of definition of Levermore's five-moment system
    • MR 99k:82063
    • Junk, M. Domain of definition of Levermore's five-moment system. J. Stat. Phys. 93 (1998), no. 5-6, 1143-1167. MR 99k:82063
    • (1998) J. Stat. Phys. , vol.93 , Issue.5-6 , pp. 1143-1167
    • Junk, M.1
  • 85
    • 0040193736 scopus 로고
    • On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
    • MR 81b:76048
    • Kawashima, S.; Matsumura, A.; Nishida, T. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation. Comm. Math. Phys. 70 (1979), no. 2, 97-124. MR 81b:76048
    • (1979) Comm. Math. Phys. , vol.70 , Issue.2 , pp. 97-124
    • Kawashima, S.1    Matsumura, A.2    Nishida, T.3
  • 86
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • MR 2000d:35018
    • Keel, M.; Tao, T. Endpoint Strichartz estimates. Amer. J. Math. 120 (1998), no. 5, 955-980. MR 2000d:35018
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 87
    • 0030534703 scopus 로고    scopus 로고
    • Moment closure hierarchies for kinetic theories
    • MR 97e:82041
    • Levermore, C. D. Moment closure hierarchies for kinetic theories. J. Statist. Phys. 83 (1996), no. 5-6, 1021-1065. MR 97e:82041
    • (1996) J. Statist. Phys. , vol.83 , Issue.5-6 , pp. 1021-1065
    • Levermore, C.D.1
  • 88
    • 0000834860 scopus 로고
    • Compactness in Boltzmann Equation via Fourier integral operators and applications. Part I and II
    • Lions, P.-L.; Compactness in Boltzmann Equation via Fourier integral operators and applications. Part I and II J. Math. Kyoto Univ., 34(2) (1994) 1-61 and Part III J. Math. Kyoto Univ., 34(3) (1994) 539-584. MR 96f:35133, MR 96f:35134
    • (1994) J. Math. Kyoto Univ. , vol.34 , Issue.2 , pp. 1-61
    • Lions, P.-L.1
  • 89
    • 0001255798 scopus 로고
    • Compactness in Boltzmann Equation via Fourier integral operators and applications. Part III
    • MR 96f:35133, MR 96f:35134
    • Lions, P.-L.; Compactness in Boltzmann Equation via Fourier integral operators and applications. Part I and II J. Math. Kyoto Univ., 34(2) (1994) 1-61 and Part III J. Math. Kyoto Univ., 34(3) (1994) 539-584. MR 96f:35133, MR 96f:35134
    • (1994) J. Math. Kyoto Univ. , vol.34 , Issue.3 , pp. 539-584
  • 90
    • 0032043665 scopus 로고    scopus 로고
    • Régularité optimale des moyennes en vitesses. II
    • French. MR 99m:35252
    • Lions, P.-L. Régularité optimale des moyennes en vitesses. II. (French) [Optimal regularity of velocity averages. II] C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 8, 945-948. MR 99m:35252
    • (1998) C. R. Acad. Sci. Paris Sér. I Math. , vol.326 , Issue.8 , pp. 945-948
    • Lions, P.-L.1
  • 91
    • 0035616508 scopus 로고    scopus 로고
    • From the Boltzmann equations to the equations of incompressible fluid mechanics I, II
    • MR 2002m:76085
    • Lions, P.-L.; Masmoudi, N. From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II. Arch. Ration. Mech. Anal. 158 (2001), no. 3, 173-193, 195-211 MR 2002m:76085
    • (2001) Arch. Ration. Mech. Anal. , vol.158 , Issue.3 , pp. 173-193
    • Lions, P.-L.1    Masmoudi, N.2
  • 92
    • 0001515315 scopus 로고
    • Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system
    • MR 92e:35160
    • Lions, P.-L.; Perthame, B. Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105 (1991), no. 2, 415-430. MR 92e:35160
    • (1991) Invent. Math. , vol.105 , Issue.2 , pp. 415-430
    • Lions, P.-L.1    Perthame, B.2
  • 93
  • 94
    • 84968518243 scopus 로고
    • A kinetic formulation of multidimensional scalar conservation laws and related equations
    • MR 94d:35100
    • Lions, P.-L.; Perthame, B.; Tadmor, E. A kinetic formulation of multidimensional scalar conservation laws and related equations. J. Amer. Math. Soc. 7 (1994), 169-191. MR 94d:35100
    • (1994) J. Amer. Math. Soc. , vol.7 , pp. 169-191
    • Lions, P.-L.1    Perthame, B.2    Tadmor, E.3
  • 97
    • 0034348887 scopus 로고    scopus 로고
    • On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
    • MR 2001f:45013
    • Mischler, S. On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system. Comm. Math. Phys. 210 (2000), no. 2, 447-466. MR 2001f:45013
    • (2000) Comm. Math. Phys. , vol.210 , Issue.2 , pp. 447-466
    • Mischler, S.1
  • 99
    • 0038500203 scopus 로고    scopus 로고
    • On the spatially homogeneous Boltzmann equation
    • MR 2000f:35147
    • Mischler, S.; Wennberg, B. On the spatially homogeneous Boltzmann equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 4, 467-501. MR 2000f:35147
    • (1999) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.16 , Issue.4 , pp. 467-501
    • Mischler, S.1    Wennberg, B.2
  • 100
    • 0039895644 scopus 로고    scopus 로고
    • High field limit for the Vlasov-Poisson-Fokker-Planck system
    • MR 2002g:82050
    • Nieto, J.; Poupaud, F.; Soler, J. High field limit for the Vlasov-Poisson-Fokker-Planck system. Arch. Ration. Mech. Anal. 158 (2001), no. 1, 29-59. MR 2002g:82050
    • (2001) Arch. Ration. Mech. Anal. , vol.158 , Issue.1 , pp. 29-59
    • Nieto, J.1    Poupaud, F.2    Soler, J.3
  • 101
    • 0023746235 scopus 로고
    • Models of dispersal in biological systems
    • MR 90a:92064
    • Othmer, H. G.; Dunbar, S. R.; Alt, W. Models of dispersal in biological systems, J. Math. Biol., 26(3) 263-298 (1988). MR 90a:92064
    • (1988) J. Math. Biol. , vol.26 , Issue.3 , pp. 263-298
    • Othmer, H.G.1    Dunbar, S.R.2    Alt, W.3
  • 102
    • 0442284502 scopus 로고    scopus 로고
    • Waves and Transport
    • Amer. Math. Soc., Providence, RI. MR 99k:73063
    • Papanicolaou, G.; Ryzhik, L. Waves and Transport. IAS/Park City Mathematics series. Volume 5, Amer. Math. Soc., Providence, RI, 1999. MR 99k:73063
    • (1999) IAS/Park City Mathematics Series , vol.5
    • Papanicolaou, G.1    Ryzhik, L.2
  • 103
    • 0002288656 scopus 로고    scopus 로고
    • Time decay, propagation of low moments and dispersive effects for kinetic equations
    • MR 97e:82042
    • Perthame, B. Time decay, propagation of low moments and dispersive effects for kinetic equations. Comm. Partial Differential Equations 21 (1996), no. 3-4, 659-686. MR 97e:82042
    • (1996) Comm. Partial Differential Equations , vol.21 , Issue.3-4 , pp. 659-686
    • Perthame, B.1
  • 104
    • 2142715844 scopus 로고    scopus 로고
    • Kinetic formulation of conservation laws
    • Oxford Univ. Press
    • Perthame, B. Kinetic formulation of conservation laws. Oxford Univ. Press, Series in Math. and Appl. 21 (2002).
    • (2002) Series in Math. and Appl. , vol.21
    • Perthame, B.1
  • 105
    • 0032114290 scopus 로고    scopus 로고
    • A limiting case of velocity averaging lemmas
    • MR 99h:82064
    • Perthame, B.; Souganidis, P. E. A limiting case of velocity averaging lemmas. Ann. Sc. E.N.S. Série 4, 31 (1998) 591-598. MR 99h:82064
    • (1998) Ann. Sc. E.N.S. Série 4 , vol.31 , pp. 591-598
    • Perthame, B.1    Souganidis, P.E.2
  • 106
    • 0033145381 scopus 로고    scopus 로고
    • Morrey-Campanato estimates for Helmholtz Equations
    • MR 2000i:35023
    • Perthame, B.; Vega, L. Morrey-Campanato estimates for Helmholtz Equations. J. Funct. Anal. 164 (2) (1999), 340-355. MR 2000i:35023
    • (1999) J. Funct. Anal. , vol.164 , Issue.2 , pp. 340-355
    • Perthame, B.1    Vega, L.2
  • 107
    • 0038648304 scopus 로고    scopus 로고
    • Sommerfeld condition for a Liouville equation and concentration of trajectories
    • Perthame, B.; Vega, L. Sommerfeld condition for a Liouville equation and concentration of trajectories. Bull, of Braz. Math. Soc., New Series 34(1), 1-15 (2003).
    • (2003) Bull, of Braz. Math. Soc., New Series , vol.34 , Issue.1 , pp. 1-15
    • Perthame, B.1    Vega, L.2
  • 108
    • 84983941745 scopus 로고
    • Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory
    • MR 93h:82074
    • Poupaud, F. Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory. Z. Angew. Math. Mech. 72 (1992), no. 8, 359-372. MR 93h:82074
    • (1992) Z. Angew. Math. Mech. , vol.72 , Issue.8 , pp. 359-372
    • Poupaud, F.1
  • 109
    • 44049119012 scopus 로고
    • Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
    • MR 93d:35170
    • Pfaffelmoser, K. Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Differential Equations 95 (1992), no. 2, 281-303. MR 93d:35170
    • (1992) J. Differential Equations , vol.95 , Issue.2 , pp. 281-303
    • Pfaffelmoser, K.1
  • 110
    • 0030127191 scopus 로고    scopus 로고
    • Kinetic theory for bubbly flow I: Collisionless case and II: Fluid dynamic limit
    • MR 97f:82042, MR 97f:82043
    • Russo, G.; Smereka, P. Kinetic theory for bubbly flow I: collisionless case and II: fluid dynamic limit. SIAM J. Appl. Math., 56 (1996), no.2, 327-357 and 358-371. MR 97f:82042, MR 97f:82043
    • (1996) SIAM J. Appl. Math. , vol.56 , Issue.2 , pp. 327-357
    • Russo, G.1    Smereka, P.2
  • 111
    • 0034364359 scopus 로고    scopus 로고
    • The gyrokinetic approximation for the Vlasov-Poisson system
    • MR 2001h:82096
    • Saint-Raymond, L. The gyrokinetic approximation for the Vlasov-Poisson system. Math. Models Methods Appl. Sci. 10 (2000), no. 9, 1305-1332. MR 2001h:82096
    • (2000) Math. Models Methods Appl. Sci. , vol.10 , Issue.9 , pp. 1305-1332
    • Saint-Raymond, L.1
  • 112
    • 0001072016 scopus 로고
    • Global existence of smooth solutions to the Vlasov-Poisoon system in three dimensions
    • MR 92g:82113
    • Schaeffer, J. Global existence of smooth solutions to the Vlasov-Poisoon system in three dimensions, Comm. P.D.E., 16, 1313-1335 (1991). MR 92g:82113
    • (1991) Comm. P.D.E. , vol.16 , pp. 1313-1335
    • Schaeffer, J.1
  • 114
    • 0034549474 scopus 로고    scopus 로고
    • One-dimensional kinetic models of granular flows
    • MR 2002a:82094
    • Toscani, G. One-dimensional kinetic models of granular flows. M2AN Math. Model. Numer. Anal. 34 (2000), no. 6, 1277-1291. MR 2002a:82094
    • (2000) M2AN Math. Model. Numer. Anal. , vol.34 , Issue.6 , pp. 1277-1291
    • Toscani, G.1
  • 115
    • 0003603398 scopus 로고
    • Fundamentals of Maxwell's kinetic theory of a simple monatomic gas. Treated as a branch of rational mechanics
    • Academic Press, New York-London. MR 81f:80001
    • Truesdell, C.; Muncaster, R. G. Fundamentals of Maxwell's kinetic theory of a simple monatomic gas. Treated as a branch of rational mechanics. Pure and Applied Mathematics, 83. Academic Press, New York-London, 1980. MR 81f:80001
    • (1980) Pure and Applied Mathematics , vol.83
    • Truesdell, C.1    Muncaster, R.G.2
  • 116
    • 0038460461 scopus 로고    scopus 로고
    • The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem. Recent topics in mathematics moving toward science and engineering
    • MR 2002e:82057
    • Ukai, S. The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem. Recent topics in mathematics moving toward science and engineering. Japan J. Indust. Appl. Math. 18 (2001), no. 2, 383-392. MR 2002e:82057
    • (2001) Japan J. Indust. Appl. Math. , vol.18 , Issue.2 , pp. 383-392
    • Ukai, S.1
  • 117
    • 0020906174 scopus 로고
    • Steady solutions of the Boltzmann equation for a gas flow past an obstacle
    • MR 85a:76079
    • Ukai, S.; Asano, K. Steady solutions of the Boltzmann equation for a gas flow past an obstacle. I. Existence. Arch. Rational Mech. Anal. 84 (1983), no. 3, 249-291. MR 85a:76079
    • (1983) I. Existence. Arch. Rational Mech. Anal. , vol.84 , Issue.3 , pp. 249-291
    • Ukai, S.1    Asano, K.2
  • 118
    • 67649344144 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • North-Holland, Amsterdam. MR 2003k:82087
    • Villani, C. A review of mathematical topics in collisional kinetic theory. Handbook of mathematical fluid dynamics, Vol. I, 71-305, North-Holland, Amsterdam, 2002. MR 2003k:82087
    • (2002) Handbook of Mathematical Fluid Dynamics , vol.1 , pp. 71-305
    • Villani, C.1
  • 119
    • 0037358153 scopus 로고    scopus 로고
    • Cercignani's conjecture is sometimes true and always almost true
    • Villani, C. Cercignani's conjecture is sometimes true and always almost true. Comm. Math. Phys. 234 (2003), no. 3, 455-490.
    • (2003) Comm. Math. Phys. , vol.234 , Issue.3 , pp. 455-490
    • Villani, C.1
  • 120
    • 0036377236 scopus 로고    scopus 로고
    • Some new velocity averaging results
    • electronic. MR 2003b:35027
    • Westdickenberg, M. Some new velocity averaging results. SIAM J. Math. Anal. 33 (2002), no. 5, 1007-1032 (electronic). MR 2003b:35027
    • (2002) SIAM J. Math. Anal. , vol.33 , Issue.5 , pp. 1007-1032
    • Westdickenberg, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.