-
1
-
-
0000224209
-
1 for the spatially homogeneous Boltzmann equation
-
1 for the spatially homogeneous Boltzmann equation. Arch. Rational Mech. Anal. 103 (1988), no. 2, 151-167.
-
(1988)
Arch. Rational Mech. Anal.
, vol.103
, Issue.2
, pp. 151-167
-
-
Arkeryd, L.1
-
2
-
-
84943150390
-
1 trend to equilibrium for the Boltzmann equation
-
1 trend to equilibrium for the Boltzmann equation. Stud. Appl. Math. 87 (1992), no. 3, 283-288.
-
(1992)
Stud. Appl. Math.
, vol.87
, Issue.3
, pp. 283-288
-
-
Arkeryd, L.1
-
3
-
-
0007406044
-
On logarithmic Sobolev inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations
-
in press
-
Arnold, A.; Markowich, P.; Toscani, G.; Unterreiter, A. On logarithmic Sobolev inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations. J. Funct. Anal., in press.
-
J. Funct. Anal.
-
-
Arnold, A.1
Markowich, P.2
Toscani, G.3
Unterreiter, A.4
-
4
-
-
0001119849
-
Diffusions hypercontractives. Séminaire de probabilités, XIX, 1983/84, 177-206
-
Springer, Berlin-New York
-
Bakry, D.; Emery, M. Diffusions hypercontractives. Séminaire de probabilités, XIX, 1983/84, 177-206. Lecture Notes in Mathematics, 1123. Springer, Berlin-New York, 1985.
-
(1985)
Lecture Notes in Mathematics, 1123
-
-
Bakry, D.1
Emery, M.2
-
6
-
-
84972497473
-
On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
-
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.
-
(1995)
Differential Integral Equations
, vol.8
, Issue.3
, pp. 487-514
-
-
Bouchut, F.1
Dolbeault, J.2
-
7
-
-
0002356751
-
Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
-
Carlen, E. A.; Carvalho, M. C. Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation. J. Statist. Phys. 67 (1992), no. 3-4, 575-608.
-
(1992)
J. Statist. Phys.
, vol.67
, Issue.3-4
, pp. 575-608
-
-
Carlen, E.A.1
Carvalho, M.C.2
-
8
-
-
21344493381
-
Entropy production estimates for Boltzmann equations with physically realistic collision kernels
-
Carlen, E. A.; Carvalho, M. C. Entropy production estimates for Boltzmann equations with physically realistic collision kernels. J. Statist. Phys. 74 (1994), no. 3-4, 743-782.
-
(1994)
J. Statist. Phys.
, vol.74
, Issue.3-4
, pp. 743-782
-
-
Carlen, E.A.1
Carvalho, M.C.2
-
9
-
-
0003200990
-
The mathematical theory of dilute gases
-
Springer, New York
-
Cercignani, C.; Illner, R.; Pulvirenti, M. The mathematical theory of dilute gases. Applied Mathematical Sciences, 106. Springer, New York, 1994.
-
(1994)
Applied Mathematical Sciences
, pp. 106
-
-
Cercignani, C.1
Illner, R.2
Pulvirenti, M.3
-
10
-
-
4243219284
-
La condition d'hypoellipticité d'hörmander
-
Chaleyat-Maurel, M. La condition d'hypoellipticité d'Hörmander. Astérisque 84-85 (1981), 189-202.
-
(1981)
Astérisque
, vol.84-85
, pp. 189-202
-
-
Chaleyat-Maurel, M.1
-
11
-
-
0000489740
-
Information-type measures of difference of probability distributions and indirect observations
-
Csiszár, I. Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar. 2 (1967), 299-318.
-
(1967)
Studia Sci. Math. Hungar.
, vol.2
, pp. 299-318
-
-
Csiszár, I.1
-
12
-
-
0002931582
-
Convergence to equilibrium in large time for Boltzmann and B.G.K. Equations
-
Desvillettes, L. Convergence to equilibrium in large time for Boltzmann and B.G.K. equations. Arch. Rational Mech. Anal. 110 (1990), no. 1, 73-91.
-
(1990)
Arch. Rational Mech. Anal.
, vol.110
, Issue.1
, pp. 73-91
-
-
Desvillettes, L.1
-
13
-
-
67649350730
-
Convergence to equilibrium in various situations for the solution of the Boltzmann equation
-
Nonlinear kinetic theory and mathematical aspects of hyperbolic systems (Rapallo, 1992), 101-114. World Scientific, River Edge, N.J.
-
Desvillettes, L. Convergence to equilibrium in various situations for the solution of the Boltzmann equation. Nonlinear kinetic theory and mathematical aspects of hyperbolic systems (Rapallo, 1992), 101-114. Series on Advances in Mathematics for Applied Sciences, 9. World Scientific, River Edge, N.J., 1992.
-
(1992)
Series on Advances in Mathematics for Applied Sciences
, pp. 9
-
-
Desvillettes, L.1
-
14
-
-
21844483733
-
About the regularizing properties of the non-cut-off Kac equation
-
Desvillettes, L. About the regularizing properties of the non-cut-off Kac equation. Comm. Math. Phys. 168 (1995), no. 2, 417-440.
-
(1995)
Comm. Math. Phys.
, vol.168
, Issue.2
, pp. 417-440
-
-
Desvillettes, L.1
-
15
-
-
0000278898
-
On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness
-
Desvillettes, L.; Villani, C. On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness. Comm. Partial Differential Equations 25 (2000), no. 1-2, 179-259.
-
(2000)
Comm. Partial Differential Equations
, vol.25
, Issue.1-2
, pp. 179-259
-
-
Desvillettes, L.1
Villani, C.2
-
16
-
-
0000278899
-
On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications
-
Desvillettes, L., and Villani, C. On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications. Comm. Partial Differential Equations 25 (2000), no. 1-2, 261-298.
-
(2000)
Comm. Partial Differential Equations
, vol.25
, Issue.1-2
, pp. 261-298
-
-
Desvillettes, L.1
Villani, C.2
-
18
-
-
0007362455
-
On Boltzmann's H-theorem
-
Grad, H. On Boltzmann's H-theorem. J. Soc. Indust. Appl. Math. 13 (1965), 259-277.
-
(1965)
J. Soc. Indust. Appl. Math.
, vol.13
, pp. 259-277
-
-
Grad, H.1
-
19
-
-
0001429116
-
Logarithmic Sobolev inequalities
-
Gross, L. Logarithmic Sobolev inequalities. Amer. J. Math. 97 (1975), no. 4, 1061-1083.
-
(1975)
Amer. J. Math.
, vol.97
, Issue.4
, pp. 1061-1083
-
-
Gross, L.1
-
20
-
-
0002236459
-
Logarithmic Sobolev inequalities and contractivity properties of semigroups
-
Dirichlet forms (Varenna, 1992), 54-88. Springer, Berlin
-
Gross, L. Logarithmic Sobolev inequalities and contractivity properties of semigroups. Dirichlet forms (Varenna, 1992), 54-88. Lecture Notes in Mathematics, 1563. Springer, Berlin, 1993.
-
(1993)
Lecture Notes in Mathematics
, pp. 1563
-
-
Gross, L.1
-
21
-
-
15244346736
-
Hypoelliptic second order differential equations
-
Hörmander, L. Hypoelliptic second order differential equations. Acta Math. 119 (1967), 147-171.
-
(1967)
Acta Math.
, vol.119
, pp. 147-171
-
-
Hörmander, L.1
-
22
-
-
0000170568
-
On a class of ultraparabolic equations
-
Il'in, A. M. On a class of ultraparabolic equations. Dokl. Akad. Nauk SSSR 159 (1964), 1214-1217; Sov. Math. Dokl. 5 (1964), 1673-1676.
-
(1964)
Dokl. Akad. Nauk SSSR
, vol.159
, pp. 1214-1217
-
-
Il'in, A.M.1
-
23
-
-
0002389336
-
-
Il'in, A. M. On a class of ultraparabolic equations. Dokl. Akad. Nauk SSSR 159 (1964), 1214-1217; Sov. Math. Dokl. 5 (1964), 1673-1676.
-
(1964)
Sov. Math. Dokl.
, vol.5
, pp. 1673-1676
-
-
-
24
-
-
0002460456
-
Pseudo-differential operators and hypoellipticity. Partial differential equations
-
Univ. California, Berkeley, Calif., 1971, Amererican Mathematical Society, Providence, R.I.
-
Kohn, J. J. Pseudo-differential operators and hypoellipticity. Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971), 61-69. Amererican Mathematical Society, Providence, R.I., 1973.
-
(1973)
Proc. Sympos. Pure Math.
, vol.23
, pp. 61-69
-
-
Kohn, J.J.1
-
25
-
-
84941465845
-
A lower bound for discrimination information in terms of variation
-
Kullback, S. A lower bound for discrimination information in terms of variation. IEEE Trans. Information Theory 4 (1967), 126-127.
-
(1967)
IEEE Trans. Information Theory
, vol.4
, pp. 126-127
-
-
Kullback, S.1
-
26
-
-
0001156542
-
L'algèbre de lie des gradients itérés d'un générateur markovien - Développements de moyennes et d'entropies
-
Ledoux, M. L'algèbre de Lie des gradients itérés d'un générateur markovien - développements de moyennes et d'entropies. Ann. Sci. École Norm. Sup. (4) 28 (1995), no. 4, 435-460.
-
(1995)
Ann. Sci. École Norm. Sup. (4)
, vol.28
, Issue.4
, pp. 435-460
-
-
Ledoux, M.1
-
27
-
-
0000834860
-
Compactness in Boltzmann's equation via Fourier integral operators and applications, I, II, III
-
Lions, P-L. Compactness in Boltzmann's equation via Fourier integral operators and applications, I, II, III. J. Math. Kyoto Univ. 34 (1994), 391-427, 429-461, no. 2, 539-584.
-
(1994)
J. Math. Kyoto Univ.
, vol.34
, pp. 391-427
-
-
Lions, P.-L.1
-
28
-
-
0033408149
-
Spatial decay solutions of the Boltzmann equation: Converse properties of long time limiting behavior
-
Lu, X. Spatial decay solutions of the Boltzmann equation: converse properties of long time limiting behavior. SIAM J. Math. Anal. 30 (1999), no. 5, 1151-1174.
-
(1999)
SIAM J. Math. Anal.
, vol.30
, Issue.5
, pp. 1151-1174
-
-
Lu, X.1
-
29
-
-
0031488084
-
Boltzmann equation with infinite energy: Renormalized solutions and distributional solutions for small initial data and initial data close to a Maxwellian
-
Mischler, S.; Perthame, B. Boltzmann equation with infinite energy: renormalized solutions and distributional solutions for small initial data and initial data close to a Maxwellian. SIAM J. Math. Anal. 28 (1997), no. 5, 1015-1027.
-
(1997)
SIAM J. Math. Anal.
, vol.28
, Issue.5
, pp. 1015-1027
-
-
Mischler, S.1
Perthame, B.2
-
30
-
-
0001070817
-
Scaling limit for interacting Ornstein-Uhlenbeck processes
-
Olla, S.; Varadhan, S. R. S. Scaling limit for interacting Ornstein-Uhlenbeck processes. Comm. Math. Phys. 135 (1991), no. 2, 355-378.
-
(1991)
Comm. Math. Phys.
, vol.135
, Issue.2
, pp. 355-378
-
-
Olla, S.1
Varadhan, S.R.S.2
-
32
-
-
0003299394
-
The Fokker-Planck equation
-
Springer Series in Synergetics, 18. Springer, Berlin-New York
-
Risken, H. The Fokker-Planck equation. Methods of solution and applications. Second edition. Springer Series in Synergetics, 18. Springer, Berlin-New York, 1989.
-
(1989)
Methods of Solution and Applications. Second Edition
-
-
Risken, H.1
-
33
-
-
12944295719
-
Some inequalities satisfied by the quantities of information of Fisher and Shannon
-
Stam, A. Some inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control 2 (1959), 101-112.
-
(1959)
Information and Control
, vol.2
, pp. 101-112
-
-
Stam, A.1
-
34
-
-
0007365295
-
H-theorem and asymptotic trend of the solution for a rarefied gas in the vacuum
-
Toscani, G. H-theorem and asymptotic trend of the solution for a rarefied gas in the vacuum. Arch. Rational Mech. Anal. 100 (1987), no. 1, 1-12.
-
(1987)
Arch. Rational Mech. Anal.
, vol.100
, Issue.1
, pp. 1-12
-
-
Toscani, G.1
-
35
-
-
0032632377
-
Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
-
Toscani, G. Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation. Quart. Appl. Math. 57 (1999), no. 3, 521-541.
-
(1999)
Quart. Appl. Math.
, vol.57
, Issue.3
, pp. 521-541
-
-
Toscani, G.1
-
36
-
-
0033242961
-
Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
-
Toscani, G.; Villani, C. Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Comm. Math. Phys. 203 (1999), no. 3, 667-706.
-
(1999)
Comm. Math. Phys.
, vol.203
, Issue.3
, pp. 667-706
-
-
Toscani, G.1
Villani, C.2
-
37
-
-
0034147246
-
On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds
-
Toscani, G.; Villani, C. On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. J. Statist. Phys. 98 (2000), no. 5-6, 1279-1309.
-
(2000)
J. Statist. Phys.
, vol.98
, Issue.5-6
, pp. 1279-1309
-
-
Toscani, G.1
Villani, C.2
-
38
-
-
0003603398
-
Fundamentals of Maxwell's kinetic theory of a simple monoatomic gas
-
Academic Press, New York-London
-
Truesdell, C.; Muncaster, R. G. Fundamentals of Maxwell's kinetic theory of a simple monoatomic gas. Pure and Applied Mathematics, 83. Academic Press, New York-London, 1980.
-
(1980)
Pure and Applied Mathematics, 83.
-
-
Truesdell, C.1
Muncaster, R.G.2
-
39
-
-
0002952245
-
The fundamental solution of a degenerate partial differential equation of parabolic type
-
Weber, M. The fundamental solution of a degenerate partial differential equation of parabolic type. Trans. Amer. Math. Soc. 71 (1951), 24-37.
-
(1951)
Trans. Amer. Math. Soc.
, vol.71
, pp. 24-37
-
-
Weber, M.1
|