Funzionali entropia ed equilibrio di sistemi di molte particelle
Bollettino dell'Unione Matematica Italiana (2008)
- Volume: 1, Issue: 3, page 509-524
- ISSN: 0392-4041
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topToscani, G.. "Funzionali entropia ed equilibrio di sistemi di molte particelle." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 509-524. <http://eudml.org/doc/290482>.
@article{Toscani2008,
author = {Toscani, G.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {10},
number = {3},
pages = {509-524},
publisher = {Unione Matematica Italiana},
title = {Funzionali entropia ed equilibrio di sistemi di molte particelle},
url = {http://eudml.org/doc/290482},
volume = {1},
year = {2008},
}
TY - JOUR
AU - Toscani, G.
TI - Funzionali entropia ed equilibrio di sistemi di molte particelle
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 509
EP - 524
LA - ita
UR - http://eudml.org/doc/290482
ER -
References
top- ARNOLD, A. - MARKOWICH, P. A. - TOSCANI, G. - UNTERREITER, A., On Convex Sobolev Inequalities and the Rate of Convergence to Equilibrium for Fokker-Planck Type Equations. Comm. Partial Differential Equations, 26 (2001), 43-100. Zbl0982.35113MR1842428DOI10.1081/PDE-100002246
- ARNOLD, A. - MARKOWICH, P.A. - TOSCANI, G. - UNTERREITER, A., On Generalized Csiszar-Kullback Inequalities. Monatsh. Math., 131 (2000), 235-253. Zbl1015.94003MR1801751DOI10.1007/s006050070013
- BAKRY, D. - EMERY, M., Diffusions hypercontractives. In Sém. Proba. XIX, 1123Lecture Notes in Math.Springer, 1985, 177-206. MR889476DOI10.1007/BFb0075847
- BERNIS, F. - FRIEDMAN, A., Higher order nonlinear degenerate parabolic equations, J. Diff. Eqns.83 (1990), 179-206. Zbl0702.35143MR1031383DOI10.1016/0022-0396(90)90074-Y
- BOBYLEV, A.V., The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules. Mathematical physics reviews, 7 (1988), 111-233. Zbl0850.76619MR1128328
- BOLTZMANN, L., Weitere Studien uber das Warmegleichgewicht unter Gasmolekulen. Sitz. der Akademie der Wissenschaften66, (1872), 275-370 , Lectures on Gas Theory. University of California Press, Berkeley, 1964. Translated by S.G. Brush. Reprint of the 1896-1898 Edition. Reprinted by Dover Publications, 1995.
- BHATNAGAR, P.L. - GROSS, E.P. - KROOK, M., A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511-525. Zbl0055.23609
- CÁCERES, M.J. - CARRILLO, J.A. - TOSCANI, G., Long-time behavior for a nonlinear fourth-order parabolic equation. Trans. Amer. Math. Soc., 357 (2005), 1161-1175. Zbl1077.35028MR2110436DOI10.1090/S0002-9947-04-03528-7
- CARLEN, E.A. - CARVALHO, M., Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation. J. Statist. Phys., 67 (1992), 575-608. Zbl0899.76317MR1171145DOI10.1007/BF01049721
- CARRILLO, J.A. - JUENGEL, A. - MARKOWICH, P. - TOSCANI, G. - UNTERREITER, A., Entropy production methods for degenerate parabolic problems and generalized Sobolev inequalities. Monatsh. Math., 133 (2001) 1-82. Zbl0984.35027MR1853037DOI10.1007/s006050170032
- CARRILLO, J.A. - LEDERMAN, C. - MARKOWICH, P.A. - TOSCANI, G., Poincarè Inequalities for Linearizations of Very Fast Diffusion Equations., Nonlinearity, 15 (2001), 1-16. Zbl1011.35025MR1901093DOI10.1088/0951-7715/15/3/303
- CARRILLO, J.A. - MCCANN, R.J. - VILLANI, C., Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana, 19 (2003), 1-48. Zbl1073.35127MR2053570DOI10.4171/RMI/376
- CARRILLO, J.A. - TOSCANI, G., Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations. Mathem. Methods Appl. Sciences, 21 (1998), 1269-1286. Zbl0922.35131MR1639292DOI10.1002/(SICI)1099-1476(19980910)21:13<1269::AID-MMA995>3.3.CO;2-F
- CARRILLO, J.A. - TOSCANI, G., Asymptotic -decay of the porous medium equation to self-similarity. Indiana Univ. Math. J., 46 (2000), 113-142. Zbl0963.35098MR1777035DOI10.1512/iumj.2000.49.1756
- CARRILLO, J.A. - TOSCANI, G., Large-time asymptotics for strong solutions of the thin film equation. Commun. Math. Phys., 225 (2002), 113-142. Zbl0990.35054MR1888873DOI10.1007/s002200100591
- CARRILLO, J.A. - VÁZQUEZ, J.L., Fine asymptotics for fast diffusion equations. Comm. Partial Differential Equations, 28 (2003), 1023-1056. Zbl1036.35100MR1986060DOI10.1081/PDE-120021185
- CARRILLO, J.A. - VÁZQUEZ, J.L., Asymptotic complexity in filtration equations. J. Evol. Equ., 7 (2007), 471-495. MR2328935DOI10.1007/s00028-006-0298-z
- CERCIGNANI, C., H-theorem and trend to equilibrium in the kinetic theory of gases. Arch. Mech., 34 (1982), 231-241. Zbl0538.76068MR715658
- CERCIGNANI, C., Mathematical methods in kinetic theory. Second edition. Plenum Press, New York, 1990. Zbl0726.76083MR1069558DOI10.1007/978-1-4899-7291-0
- CHERASEKHAR, S., Principles of Stellar Dynamics. Courier Dover Publ.New York, 1942
- COVER, T.M. - THOMAS, J.A., Elements of Information Theory. J. Wiley & Sons Inc., New York, 1991. Zbl0762.94001MR1122806DOI10.1002/0471200611
- CSISZAR, I., Information-type measures of difference of probability distributions and indirect observations. Stud. Sci. Math. Hung., 2 (1967), 299-318. Zbl0157.25802MR219345
- DESVILLETTES, L., Entropy production rate and convergence in kinetic equations. Comm. Math. Phys., 26 (1989), 687-702. Zbl0688.76057MR1006301
- DESVILLETTES, L. - VILLANI, C., On the Spatially Homogeneous Landau Equation for Hard Potentials. Part II: H-Theorem and Applications. Comm. Partial Differential Equations25, n. 1-2 (2000), 261-298. Zbl0951.35130MR1737548DOI10.1080/03605300008821513
- 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), 1-42. Zbl1029.82032MR1787105DOI10.1002/1097-0312(200101)54:1<1::AID-CPA1>3.0.CO;2-Q
- DESVILLETTES, L. - VILLANI, C., On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Invent. Math., 159 (2005), 245-316. Zbl1162.82316MR2116276DOI10.1007/s00222-004-0389-9
- DIPERNA, R.J., Compensated compactness and general systems of conservation laws. Trans. Amer. Math. Soc., 292 (1985), 383-420. Zbl0606.35052MR808729DOI10.2307/2000221
- DIPERNA, R.J. - LIONS, P.L., On the Cauchy problem for the Boltzmann equation: Global existence and weak stability. Ann. of Math. (2) 130 (1989), 312-366. Zbl0698.45010MR1014927DOI10.2307/1971423
- FISHER, R., Theory of statistical estimation. Math. Proc. Cambridge Philos. Soc., 22 (1925), 700-725. Zbl51.0385.01
- GABETTA, E. - MARKOWICH, P.A. - UNTERREITER, A., A note on the entropy production of the radiative transfer equation. Appl. Math. Lett., 12 (1999), 111-116. Zbl0939.35035MR1750607DOI10.1016/S0893-9659(99)00044-0
- GIANAZZA, U. - SAVARÉ, G. - TOSCANI, G., The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation. Arch. Rat. Mech. Anal. (in press). MR2533926DOI10.1007/s00205-008-0186-5
- GROSS, L., Logarithmic Sobolev inequalities. Amer. J. of Math., 97 (1975), 1061-1083. Zbl0318.46049MR420249DOI10.2307/2373688
- JUENGEL, A. - MARKOWICH, P. - TOSCANI, G., Decay rates for solutions of degenerate parabolic systems. Electron. J. Diff. Eqs. Conf., 06 (2001), 189-202. Zbl0964.35085MR1804774
- JUENGEL, A. - MATTHES, D., An algorithmic construction of entropies in higher-order nonlinear PDEs. Nonlinearity, 19 (2006), 633-659. Zbl1091.35031MR2209292DOI10.1088/0951-7715/19/3/006
- JUENGEL, A. - TOSCANI, G., Exponential decay in time of solutions to a nonlinear fourth-order parabolic equation. Z. Angew. Math. Phys., 54 (2003), 377-386. Zbl1029.35033MR2048659DOI10.1007/s00033-003-1026-y
- KULLBACK, S., A lower bound for discrimination information in terms of variation. IEEE Trans. Inf. The., 4 (1967), 126-127.
- LANDAU, L., Die kinetische Gleichung fur den Fall Coulombscher Wechselwirkung. Phys. Z. Sovjet., 10 (1936), 154-164. Zbl0015.38202
- LAX, P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, 11. Society for Industrial and Applied Mathematics, Philadelphia, Pa., (1973), v+48. Zbl0268.35062MR350216
- LEDERMAN, C. - MARKOWICH, P.A., On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass. Comm. Partial Differential Equations, 28 (2003), 301-332. Zbl1024.35040MR1974458DOI10.1081/PDE-120019384
- KAMENOMOSTSKAYA, S., The asymptotic behavior of the solution of the filtration equation. Israel J. Math., 14 (1973), 76-87. Zbl0254.35054MR315292DOI10.1007/BF02761536
- MARKOWICH, P.A. - VILLANI, C., On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. Mat. Contemp., 19 (2000), 1-29. Zbl1139.82326MR1812873
- NASH, J., Continuity of solutions of parabolic and elliptic equations. Amer. J. Math., 80 (1958), 931-954. Zbl0096.06902MR100158DOI10.2307/2372841
- OTTO, F., The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Diff. Eq., 26 (2001), 101-174. Zbl0984.35089MR1842429DOI10.1081/PDE-100002243
- RISKEN, H., The Fokker-Planck equation. Methods of solution e applications. Second edition. Springer Series in Synergetics, 18Springer-Verlag, Berlin, 1989. Zbl0665.60084MR987631DOI10.1007/978-3-642-61544-3
- SHANNON, C.E., Collected papers. Edited by N. J. A. Sloane e Aaron D. Wyner. IEEE Press, New York, 1993. Zbl0846.01022MR1216351
- STAM, A., Some inequalities satisfied by the quantities of information of Fisher and Shannon. Inform. Control, 2 (1959), 101-112. Zbl0085.34701MR109101
- TOSCANI, G., Sur l'inégalité logarithmique de Sobolev. C.R. Acad. Sc. Paris, 324 (1997), 689-694. MR1447044DOI10.1016/S0764-4442(97)86991-1
- TOSCANI, G., Remarks on entropy and equilibrium states. Appl. Math. Letters, 12 (1999), 19-25. Zbl0940.35168MR1750055DOI10.1016/S0893-9659(99)00096-8
- TOSCANI, G. - VILLANI, C., Sharp entropy production bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Commun. Math. Phys.203 (1999), 667-706. Zbl0944.35066MR1700142DOI10.1007/s002200050631
- TOSCANI, G. - VILLANI, C., Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Statist. Phys., 94 (1999), 619-637. Zbl0958.82044MR1675367DOI10.1023/A:1004589506756
- TOSCANI, G. - VILLANI, C., On the trend to equilibrium for some dissipative systems with slowing increasing a priori bounds. J. Statist. Phys., 98 (2000), 1279-1309. Zbl1034.82032MR1751701DOI10.1023/A:1018623930325
- VILLANI, C., Cercignani's conjecture is sometimes true and always almost true. Commun. Math. Phys., 234 (2003), 455-490. Zbl1041.82018MR1964379DOI10.1007/s00220-002-0777-1
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