메뉴 건너뛰기




Volumn 29, Issue 1, 1998, Pages 1-17

The variational formulation of the Fokker-Planck equation

Author keywords

Fokker Planck equation; Free energy; Steepest descent; Wasserstein metric

Indexed keywords


EID: 0032343437     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096303359     Document Type: Article
Times cited : (1723)

References (24)
  • 2
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Y. BRENIER, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math., 44 (1991), pp. 375-417.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 3
    • 85053493507 scopus 로고    scopus 로고
    • Allocation maps with general cost functions
    • Partial Differential Equations and Applications, P. Marcellini, G. G. Talenti, and E. Vesintini, eds., Marcel Dekker, New York, NY
    • L. A. CAFFARELLI, Allocation maps with general cost functions, in Partial Differential Equations and Applications, P. Marcellini, G. G. Talenti, and E. Vesintini, eds., Lecture Notes in Pure and Applied Mathematics 177, Marcel Dekker, New York, NY, 1996, pp. 29-35.
    • (1996) Lecture Notes in Pure and Applied Mathematics , vol.177 , pp. 29-35
    • Caffarelli, L.A.1
  • 4
    • 0002121327 scopus 로고
    • Stochastic problems in physics and astronomy
    • S. CHANDRASEKHAR, Stochastic problems in physics and astronomy, Rev. Mod. Phys., 15 (1942), pp. 1-89.
    • (1942) Rev. Mod. Phys. , vol.15 , pp. 1-89
    • Chandrasekhar, S.1
  • 5
    • 0003908527 scopus 로고
    • Über die partiellen Differenzgleichungen der mathematischen Physik
    • R. COURANT, K. FRIEDRICHS, AND H. LEWY, Über die partiellen Differenzgleichungen der mathematischen Physik, Math. Ann., 100 (1928), pp. 1-74.
    • (1928) Math. Ann. , vol.100 , pp. 1-74
    • Courant, R.1    Friedrichs, K.2    Lewy, H.3
  • 6
    • 0030526460 scopus 로고    scopus 로고
    • Young measure solutions for a nonlinear parabolic equation of forward-backward type
    • S. DEMOULINI, Young measure solutions for a nonlinear parabolic equation of forward-backward type, SIAM J. Math. Anal., 27 (1996), pp. 376-403.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 376-403
    • Demoulini, S.1
  • 8
    • 0001073165 scopus 로고
    • Optimal maps in Mange's mass transport problems
    • W. GANGBO AND R. J. MCCANN, Optimal maps in Mange's mass transport problems, C. R. Acad. Sci. Paris, 321 (1995), pp. 1653-1658.
    • (1995) C. R. Acad. Sci. Paris , vol.321 , pp. 1653-1658
    • Gangbo, W.1    Mccann, R.J.2
  • 9
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. GANGBO AND R. J. MCCANN, The geometry of optimal transportation, Acta Math., 177 (1996), pp. 113-161.
    • (1996) Acta Math. , vol.177 , pp. 113-161
    • Gangbo, W.1    Mccann, R.J.2
  • 10
    • 0000797976 scopus 로고
    • A class of Wasserstein metrics for probability distributions
    • C. R. GIVENS AND R. M. SHORTT, A class of Wasserstein metrics for probability distributions, Michigan Math. J., 31 (1984), pp. 231-240.
    • (1984) Michigan Math. J. , vol.31 , pp. 231-240
    • Givens, C.R.1    Shortt, R.M.2
  • 11
    • 0002390876 scopus 로고
    • A statistical equilibrium model of coherent structures in magnetohydrodynamics
    • R. JORDAN, A statistical equilibrium model of coherent structures in magnetohydrodynamics, Nonlinearity, 8 (1995), pp. 585-613.
    • (1995) Nonlinearity , vol.8 , pp. 585-613
    • Jordan, R.1
  • 12
    • 67349268344 scopus 로고    scopus 로고
    • An extended variational principle
    • Partial Differential Equations and Applications, P. Marcellini, G. G. Talenti, and E. Vesintini, eds., Marcel Dekker, New York, NY
    • R. JORDAN AND D. KINDERLEHRER, An extended variational principle, in Partial Differential Equations and Applications, P. Marcellini, G. G. Talenti, and E. Vesintini, eds., Lecture Notes in Pure and Applied Mathematics 177, Marcel Dekker, New York, NY, 1996, pp. 187-200.
    • (1996) Lecture Notes in Pure and Applied Mathematics , vol.177 , pp. 187-200
    • Jordan, R.1    Kinderlehrer, D.2
  • 13
    • 85034275320 scopus 로고    scopus 로고
    • Free energy and the Fokker-Planck equation
    • to appear
    • R. JORDAN, D. KINDERLEHRER, AND F. OTTO, Free energy and the Fokker-Planck equation, Physica D., to appear.
    • Physica D
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 15
    • 0031138771 scopus 로고    scopus 로고
    • Ideal magnetofluid turbulence in two dimensions
    • R. JORDAN AND B. TURKINGTON, Ideal magnetofluid turbulence in two dimensions, J. Stat. Phys., 87 (1997), pp. 661-695.
    • (1997) J. Stat. Phys. , vol.87 , pp. 661-695
    • Jordan, R.1    Turkington, B.2
  • 16
    • 0003073394 scopus 로고
    • Weak convergence of integrands and the Young measure representation
    • D. KINDERLEHRER AND P. PEDREGAL, Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal., 23 (1992), pp. 1-19.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1-19
    • Kinderlehrer, D.1    Pedregal, P.2
  • 17
    • 34547275473 scopus 로고
    • Brownian motion in a field of force and the diffusion model of chemical reactions
    • H. A. KRAMERS, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, 7 (1940), pp. 284-304.
    • (1940) Physica , vol.7 , pp. 284-304
    • Kramers, H.A.1
  • 19
    • 85034279960 scopus 로고    scopus 로고
    • Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
    • to appear
    • F. OTTO, Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory, Archive Rat. Mech. Anal., to appear.
    • Archive Rat. Mech. Anal.
    • Otto, F.1
  • 20
    • 0030579044 scopus 로고    scopus 로고
    • 1- Contraction and uniqueness for quasilinear elliptic-parabolic equations
    • 1- contraction and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations, 131 (1996), pp. 20-38.
    • (1996) J. Differential Equations , vol.131 , pp. 20-38
    • Otto, F.1
  • 23
    • 0002044060 scopus 로고
    • Singular perturbation methods in stochastic differential equations of mathematical physics
    • Z. SCHUSS, Singular perturbation methods in stochastic differential equations of mathematical physics, SIAM Rev., 22 (1980), pp. 119-155.
    • (1980) SIAM Rev. , vol.22 , pp. 119-155
    • Schuss, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.