메뉴 건너뛰기




Volumn 234, Issue 3, 2003, Pages 455-490

Cercignani's conjecture is sometimes true and always almost true

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037358153     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0777-1     Document Type: Article
Times cited : (137)

References (47)
  • 2
    • 0036133764 scopus 로고    scopus 로고
    • On the Boltzmann equation for long-range interactions
    • Alexandre, R., Villani, C.: On the Boltzmann equation for long-range interactions. Comm. Pure Appl. Math. 55(1), 30-70 (2002)
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.1 , pp. 30-70
    • Alexandre, R.1    Villani, C.2
  • 4
    • 0002042431 scopus 로고    scopus 로고
    • On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
    • Arnold, A., Markowich, P., Toscani, G., Unterreiter, A.: On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Comm. Partial Differential Equations 26(1-2), 43-100 (2001)
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.1-2 , pp. 43-100
    • Arnold, A.1    Markowich, P.2    Toscani, G.3    Unterreiter, A.4
  • 5
    • 0001119849 scopus 로고
    • Diffusions hypercontractives
    • Sém. Proba. XIX, Berlin-Heidelberg, Newyork: Springer
    • Bakry, D., Emery, M.: Diffusions hypercontractives. In: Sém. Proba. XIX, no. 1123 in Lecture Notes in Math. Berlin-Heidelberg, Newyork: Springer, 1985, pp. 177-206
    • (1985) Lecture Notes in Math. , vol.1123 , pp. 177-206
    • Bakry, D.1    Emery, M.2
  • 6
    • 0013022264 scopus 로고    scopus 로고
    • Personal communication about his joint works with K. Ball and A. Naor
    • Barthe, F.: Personal communication about his joint works with K. Ball and A. Naor
    • Barthe, F.1
  • 7
    • 84938171492 scopus 로고
    • The convolution inequality for entropy powers
    • Blachman, N.: The convolution inequality for entropy powers. IEEE Trans. Inform. Theory 2, 267-271 (1965)
    • (1965) IEEE Trans. Inform. Theory , vol.2 , pp. 267-271
    • Blachman, N.1
  • 8
    • 0000411415 scopus 로고
    • The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules
    • Bobylev, A.: The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwellian molecules. Sov. Sci. Rev. C. Math. Phys. 7, 111-233 (1988)
    • (1988) Sov. Sci. Rev. C. Math. Phys. , vol.7 , pp. 111-233
    • Bobylev, A.1
  • 9
    • 0031231967 scopus 로고    scopus 로고
    • Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems
    • Bobylev, A.V.: Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems. J. Stat. Phys. 88(5-6), 1183-1214 (1997)
    • (1997) J. Stat. Phys. , vol.88 , Issue.5-6 , pp. 1183-1214
    • Bobylev, A.V.1
  • 10
    • 0033074299 scopus 로고    scopus 로고
    • On the rate of entropy production for the Boltzmann equation
    • Bobylev, A.V., Cercignani, C.: On the rate of entropy production for the Boltzmann equation. J. Stat. Phys. 94(3-4), 603-618 (1999)
    • (1999) J. Stat. Phys. , vol.94 , Issue.3-4 , pp. 603-618
    • Bobylev, A.V.1    Cercignani, C.2
  • 11
    • 0000273265 scopus 로고
    • Superadditivity of Fisher's information and logarithmic Sobolev inequalities
    • Carlen, E.: Superadditivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal. 101(1), 194-211 (1991)
    • (1991) J. Funct. Anal. , vol.101 , Issue.1 , pp. 194-211
    • Carlen, E.1
  • 12
    • 0002356751 scopus 로고
    • Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
    • Carlen, E., Carvalho, M.: Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation. J. Stat. Phys. 67(3-4), 575-608 (1992)
    • (1992) J. Stat. Phys. , vol.67 , Issue.3-4 , pp. 575-608
    • Carlen, E.1    Carvalho, M.2
  • 13
    • 21344493381 scopus 로고
    • Entropy production estimates for Boltzmann equations with physically realistic collision kernels
    • Carlen, E., Carvalho, M.: Entropy production estimates for Boltzmann equations with physically realistic collision kernels. J. Stat. Phys. 74(3-4), 743-782 (1994)
    • (1994) J. Stat. Phys. , vol.74 , Issue.3-4 , pp. 743-782
    • Carlen, E.1    Carvalho, M.2
  • 14
    • 0012925082 scopus 로고    scopus 로고
    • Determination of the spectral gap for Kac's master equation and related stochastic evolutions
    • Preprint
    • Carlen, E., Carvalho, M., Loss, M.: Determination of the spectral gap for Kac's master equation and related stochastic evolutions. Preprint, 2000; to appear in Acta Mathematica
    • (2000) Acta Mathematica
    • Carlen, E.1    Carvalho, M.2    Loss, M.3
  • 16
    • 0000860574 scopus 로고
    • Entropy production by block variable summation and central limit theorems
    • Carlen, E., Soffer, A.: Entropy production by block variable summation and central limit theorems. Commun. Math. Phys. 140, 339-371 (1991)
    • (1991) Commun. Math. Phys. , vol.140 , pp. 339-371
    • Carlen, E.1    Soffer, A.2
  • 18
    • 0003277699 scopus 로고    scopus 로고
    • 1-decay of solutions of the porous medium equation to self-similarity
    • 1-decay of solutions of the porous medium equation to self-similarity. Indiana Univ. Math. J. 49(1), 113-142 (2000)
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.1 , pp. 113-142
    • Carrillo, J.A.1    Toscani, G.2
  • 19
    • 0001524598 scopus 로고
    • H-theorem and trend to equilibrium in the kinetic theory of gases
    • Cercignani, C.: H-theorem and trend to equilibrium in the kinetic theory of gases. Arch. Mech. 34, 231-241 (1982)
    • (1982) Arch. Mech. , vol.34 , pp. 231-241
    • Cercignani, C.1
  • 21
    • 0003817403 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press, From basic concepts to actual calculations
    • Cercignani, C.: Rarefied Gas Dynamics. Cambridge: Cambridge University Press, 2000. From basic concepts to actual calculations
    • (2000) Rarefied Gas Dynamics
    • Cercignani, C.1
  • 23
    • 0012963924 scopus 로고    scopus 로고
    • Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
    • Del Pino, M., Dolbeault, J.: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. To appear in J. Maths Pures Appl. Available on http://www.ceremade.dauphine.fr/dolbeaul/Preprints/Preprmts.html, 2001
    • (2001) J. Maths Pures Appl.
    • Del Pino, M.1    Dolbeault, J.2
  • 24
    • 0001035667 scopus 로고
    • Entropy dissipation rate and convergence in kinetic equations
    • Desvillettes, L.: Entropy dissipation rate and convergence in kinetic equations. Commun. Math. Phys. 123(4), 687-702 (1989)
    • (1989) Commun. Math. Phys. , vol.123 , Issue.4 , pp. 687-702
    • Desvillettes, L.1
  • 26
    • 0000278899 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications
    • Desvillettes, L., Villani, C.: On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications. Comm. Partial Differential Equations 25(1-2), 261-298 (2000)
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.1-2 , pp. 261-298
    • Desvillettes, L.1    Villani, C.2
  • 27
    • 0034348847 scopus 로고    scopus 로고
    • Bounds for Kac's master equation
    • Diaconis, P., Saloff-Coste, L.: Bounds for Kac's master equation. Commun. Math. Phys. 209(3), 729-755 (2000)
    • (2000) Commun. Math. Phys. , vol.209 , Issue.3 , pp. 729-755
    • Diaconis, P.1    Saloff-Coste, L.2
  • 28
    • 0035533089 scopus 로고    scopus 로고
    • Spectral gap for Kac's model of Boltzmann equation
    • Janvresse, E.: Spectral gap for Kac's model of Boltzmann equation. Ann. Probab. 29(1), 288-304 (2001)
    • (2001) Ann. Probab. , vol.29 , Issue.1 , pp. 288-304
    • Janvresse, E.1
  • 32
    • 38249011985 scopus 로고
    • On an integral criterion for hypercontractivity of diffusion semigroups and extremal functions
    • Ledoux, M.: On an integral criterion for hypercontractivity of diffusion semigroups and extremal functions. J. Funct. Anal. 105(2), 444-465 (1992)
    • (1992) J. Funct. Anal. , vol.105 , Issue.2 , pp. 444-465
    • Ledoux, M.1
  • 33
    • 0013022265 scopus 로고    scopus 로고
    • The eigenvalues of Kac's master equation
    • Maslen, D.: The eigenvalues of Kac's master equation. To appear in Math. Zeit.
    • Math. Zeit.
    • Maslen, D.1
  • 35
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • Otto, F.: The geometry of dissipative evolution equations: The porous medium equation. Comm. Partial Differential Equations 26(1-2), 101-174 (2001)
    • (2001) Comm. Partial Differential Equations , vol.26 , Issue.1-2 , pp. 101-174
    • Otto, F.1
  • 36
    • 12944295719 scopus 로고
    • 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. Inform. Control 2, 101-112 (1959)
    • (1959) Inform. Control , vol.2 , pp. 101-112
    • Stam, A.1
  • 37
    • 34250138528 scopus 로고
    • Equations de type de Boltzmann, spatialement homogènes
    • Sznitman, A.: Equations de type de Boltzmann, spatialement homogènes. Z. Wahrsch. Verw. Gebiete 66, 559-562 (1984)
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.66 , pp. 559-562
    • Sznitman, A.1
  • 39
    • 0033242961 scopus 로고    scopus 로고
    • 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. Commun. Math. Phys. 203(3), 667-706 (1999)
    • (1999) Commun. Math. Phys. , vol.203 , Issue.3 , pp. 667-706
    • Toscani, G.1    Villani, C.2
  • 40
    • 0034147246 scopus 로고    scopus 로고
    • 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. Stat. Phys. 98(5-6), 1279-1309 (2000)
    • (2000) J. Stat. Phys. , vol.98 , Issue.5-6 , pp. 1279-1309
    • Toscani, G.1    Villani, C.2
  • 42
    • 0012921514 scopus 로고    scopus 로고
    • A survey of mathematical topics in kinetic theory
    • S. Friedlander, D. Serre, (eds)., Elsevier
    • Villani, C.: A survey of mathematical topics in kinetic theory. To appear in Handbook of Mathematical Fluid Dynamics, S. Friedlander, D. Serre, (eds)., Elsevier
    • Handbook of Mathematical Fluid Dynamics
    • Villani, C.1
  • 43
    • 0032338727 scopus 로고    scopus 로고
    • On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations
    • Villani, C.: On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations. Arch. Rational Mech. Anal. 143(3), 273-307 (1998)
    • (1998) Arch. Rational Mech. Anal. , vol.143 , Issue.3 , pp. 273-307
    • Villani, C.1
  • 45
    • 0034227161 scopus 로고    scopus 로고
    • A short proof of the "concavity of entropy power"
    • Villani, C.: A short proof of the "concavity of entropy power". IEEE Trans. Inform. Theory 46(4), 1695-1696 (2000)
    • (2000) IEEE Trans. Inform. Theory , vol.46 , Issue.4 , pp. 1695-1696
    • Villani, C.1
  • 47
    • 0031092560 scopus 로고    scopus 로고
    • Entropy dissipation and moment production for the Boltzmann equation
    • Wennberg, B.: Entropy dissipation and moment production for the Boltzmann equation. J. Stat. Phys. 86(5-6), 1053-1066 (1997)
    • (1997) J. Stat. Phys. , vol.86 , Issue.5-6 , pp. 1053-1066
    • Wennberg, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.