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Transport Theory and Statistical Physics Volume 25, 1996 - Issue 7
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Original Articles

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

Anton Arnold Fachbereich Mathematik, Technische Universität Berlin, Straβe des 17. Juni 136 D, 10623, Berlin, Germany; Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA E-mail: [email protected]
,
Luis L. Bonilla Escuela Politécnica Superior, Universidad Carlos III de Madrid; Butarque 15;, 28911, Leganés, Spain E-mail: [email protected]
&
Peter A. Markowich Fachbereich Mathematik, Technische Universität Berlin;, Straβe des 17. Juni 136 D, 10623, Berlin, Germany E-mail: [email protected]
Pages 733-751 | Received 12 May 1995, Accepted 12 Jul 1996, Published online: 13 Sep 2006

Citations (14)

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Read on this site (2)

Anton Arnold, Peter Markowich, Giuseppe Toscani & Andreas Unterreiter. (2001) ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS. Communications in Partial Differential Equations 26:1-2, pages 43-100.
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Anton Arnold, Peter Markowich & Giuseppe Toscani. (2000) On large time asymptotics for drift-diffusion-poisson systems. Transport Theory and Statistical Physics 29:3-5, pages 571-581.
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Articles from other publishers (12)

Till D. Frank. 2020. Synergetics. Synergetics 149 182 .
S. N. Gomes & G. A. Pavliotis. (2017) Mean Field Limits for Interacting Diffusions in a Two-Scale Potential. Journal of Nonlinear Science 28:3, pages 905-941.
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ANSGAR JÜNGEL, CHRISTIAN KUEHN & LARA TRUSSARDI. (2016) A meeting point of entropy and bifurcations in cross-diffusion herding. European Journal of Applied Mathematics 28:2, pages 317-356.
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Till D. Frank. 2017. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science 1 36 .
Giambattista Giacomin & Christophe Poquet. (2015) Noise, interaction, nonlinear dynamics and the origin of rhythmic behaviors. Brazilian Journal of Probability and Statistics 29:2.
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Lorenzo Bertini, Giambattista Giacomin & Christophe Poquet. (2013) Synchronization and random long time dynamics for mean-field plane rotators. Probability Theory and Related Fields 160:3-4, pages 593-653.
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T. D. Frank. (2013) Strongly Nonlinear Stochastic Processes in Physics and the Life Sciences. ISRN Mathematical Physics 2013, pages 1-28.
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Giambattista Giacomin, Khashayar Pakdaman & Xavier Pellegrin. (2012) Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators. Nonlinearity 25:5, pages 1247-1273.
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Till D. Frank. 2009. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science 5239 5265 .
HAO WU, PETER A. MARKOWICH & SONGMU ZHENG. (2011) GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A SEMICONDUCTOR DRIFT-DIFFUSION-POISSON MODEL. Mathematical Models and Methods in Applied Sciences 18:03, pages 443-487.
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T.D. Frank. (2002) Generalized multivariate Fokker–Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics. Physics Letters A 305:3-4, pages 150-159.
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J. Soler, J. A. Carrillo & L. L. Bonilla. (1997) Asymptotic Behavior of an Initial-Boundary Value Problem for the Vlasov--Poisson--Fokker--Planck System. SIAM Journal on Applied Mathematics 57:5, pages 1343-1372.
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