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Volumn 25, Issue 7, 1996, Pages 733-751

Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

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EID: 0030376634     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411459608203544     Document Type: Article
Times cited : (11)

References (22)
  • 1
    • 0003027085 scopus 로고
    • Collective dynamics of coupled oscillators with random pinning
    • and references therein
    • S.H. Strogatz, C.M. Marcus, R.M. Westervelt and R.E. Mirollo, Collective dynamics of coupled oscillators with random pinning. Physica D 36, 23-50 (1989), and references therein.
    • (1989) Physica D , vol.36 , pp. 23-50
    • Strogatz, S.H.1    Marcus, C.M.2    Westervelt, R.M.3    Mirollo, R.E.4
  • 2
    • 0002429034 scopus 로고
    • Statistical mechanics of a nonlinear stochastic model
    • R.C. Desai and R. Zwanzig, Statistical mechanics of a nonlinear stochastic model. J. Stat. Phys. 19, 1-24 (1978).
    • (1978) J. Stat. Phys. , vol.19 , pp. 1-24
    • Desai, R.C.1    Zwanzig, R.2
  • 3
    • 34250144062 scopus 로고
    • Critical dynamics and fluctuations for a mean-field model of cooperative behavior
    • D.A. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior. J. Stat. Phys. 31, 29-85 (1933).
    • (1933) J. Stat. Phys. , vol.31 , pp. 29-85
    • Dawson, D.A.1
  • 4
    • 0038930098 scopus 로고
    • Periodic behavior of the stochastic Brusselator in the mean-field limit
    • M. Scheutzow, Periodic behavior of the stochastic Brusselator in the mean-field limit. Probab. Theor. Rel. Fields 72, 425-62 (1986).
    • (1986) Probab. Theor. Rel. Fields , vol.72 , pp. 425-462
    • Scheutzow, M.1
  • 7
    • 84956226705 scopus 로고
    • Evidence of collective behavior in cellular automata
    • H. Chaté and P. Manneville, Evidence of collective behavior in cellular automata. Europhys. Lett. 14, 409 (1991).
    • (1991) Europhys. Lett. , vol.14 , pp. 409
    • Chaté, H.1    Manneville, P.2
  • 8
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M.C. Cross and P.C. Hohenberg, Pattern formation outside of equilibrium. Rev. mod. Phys. 65, 851-1112 (1993).
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 9
    • 0000677291 scopus 로고
    • Stable nonequilibrium probability densities and phase transitions for mean-field models in the thermodynamic limit
    • L.L. Bonilla, Stable Nonequilibrium Probability Densities and Phase Transitions for Mean-Field Models in the Thermodynamic Limit. J. Stat. Phys. 46, 659-678 (1987).
    • (1987) J. Stat. Phys. , vol.46 , pp. 659-678
    • Bonilla, L.L.1
  • 10
    • 0003872810 scopus 로고
    • Springer-Verlag, Berlin, Heidelberg, New York, Tokyo
    • H. Haken, Advanced Synergetics. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo 1983.
    • (1983) Advanced Synergetics
    • Haken, H.1
  • 11
    • 0000570447 scopus 로고
    • H theorem and stability analysis for mean-field models of nonequilibrium phase transitions in stochastic systems
    • M. Shiino, H theorem and stability analysis for mean-field models of nonequilibrium phase transitions in stochastic systems. Phys. Lett. 112A, 302-306 (1985). M. Shiino, Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of mean-field type: H theorem on asymptotic approach to equilibrium and critical slowing-down of order parameter fluctuations. Phys. Rev. A 36, 2393-412 (1987).
    • (1985) Phys. Lett. , vol.112 A , pp. 302-306
    • Shiino, M.1
  • 12
    • 33645074567 scopus 로고
    • Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of mean-field type: H theorem on asymptotic approach to equilibrium and critical slowing-down of order parameter fluctuations
    • M. Shiino, H theorem and stability analysis for mean-field models of nonequilibrium phase transitions in stochastic systems. Phys. Lett. 112A, 302-306 (1985). M. Shiino, Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of mean-field type: H theorem on asymptotic approach to equilibrium and critical slowing-down of order parameter fluctuations. Phys. Rev. A 36, 2393-412 (1987).
    • (1987) Phys. Rev. A , vol.36 , pp. 2393-2412
    • Shiino, M.1
  • 13
    • 0040114277 scopus 로고
    • Dynamics of a soft-spin van Hemmen model. I. Phase and bifurcation diagrams for stationary distributions
    • L.L. Bonilla and J.M. Casado, Dynamics of a soft-spin van Hemmen model. I. Phase and bifurcation diagrams for stationary distributions. J. Stat. Phys. 56, 113-125 (1989).
    • (1989) J. Stat. Phys. , vol.56 , pp. 113-125
    • Bonilla, L.L.1    Casado, J.M.2
  • 15
    • 0001761129 scopus 로고
    • Cooperative dynamics in visual processing
    • H. Sompolinsky, D. Golomb and D. Kleinfeld, Cooperative dynamics in visual processing. Phys. Rev. A 43, 6990-7011 (1991).
    • (1991) Phys. Rev. A , vol.43 , pp. 6990-7011
    • Sompolinsky, H.1    Golomb, D.2    Kleinfeld, D.3
  • 16
    • 0038930011 scopus 로고
    • A classification of FP models and the small and large noise asymptotics
    • H. Jauslin, A classification of FP models and the small and large noise asymptotics. J. Stat. Phys. 40, 147-165 (1985).
    • (1985) J. Stat. Phys. , vol.40 , pp. 147-165
    • Jauslin, H.1
  • 17
    • 21544457630 scopus 로고
    • Seminaire Bourbaki, 40éme année, n° 699
    • P. Gerard, Solutions Globales du Probléme de Cauchy pour l'équation de Boltzmann. Seminaire Bourbaki, 40éme année, 1987-88, n° 699. R.J. DiPerna and P.L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. 130, 321-366 (1989).
    • (1987) Solutions Globales du Probléme de Cauchy pour l'Équation de Boltzmann
    • Gerard, P.1
  • 18
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • P. Gerard, Solutions Globales du Probléme de Cauchy pour l'équation de Boltzmann. Seminaire Bourbaki, 40éme année, 1987-88, n° 699. R.J. DiPerna and P.L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. of Math. 130, 321-366 (1989).
    • (1989) Ann. of Math. , vol.130 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.L.2
  • 20
    • 0001446381 scopus 로고
    • Les espaces du type de Beppo Levi
    • Grenoble
    • J. Deny and J. L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5, 305-370 (1954).
    • (1954) Ann. Inst. Fourier , vol.5 , pp. 305-370
    • Deny, J.1    Lions, J.L.2
  • 21
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • F. John, J.E. Marsden, and L. Sirovich, eds. Springer-Verlag, New York
    • R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, Vol. 68. F. John, J.E. Marsden, and L. Sirovich, eds. Springer-Verlag, New York 1988.
    • (1988) Applied Mathematical Sciences , vol.68
    • Temam, R.1
  • 22
    • 0000195197 scopus 로고
    • On long time asymptotics of the Vlasov-Poisson-Boltzmann equation
    • L. Desvillettes and J. Dolbeault, On long time asymptotics of the Vlasov-Poisson-Boltzmann equation, Comm. P.D.E., 16, 451-489 (1991).
    • (1991) Comm. P.D.E. , vol.16 , pp. 451-489
    • Desvillettes, L.1    Dolbeault, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.