Advertisement

Generalized Solutions to Nonlinear Fokker–Planck Equations with Linear Drift

  • Viorel BarbuEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

Existence and long-time behaviour of solutions to nonlinear Fokker–Planck equations (NFPEs) with linear drift are studied.

Keywords

Fokker–Planck equation Entropy Accretive Mild solution Lyapunov function 

MSC (2010)

35K55 35Q84 47H07 

References

  1. 1.
    Barbu, V.: Generalized solutions to nonlinear Fokker-Plank equations. J. Differ. Equ. 261, 2446–2471 (2016)CrossRefGoogle Scholar
  2. 2.
    Benilan, Ph, Crandall, M.G.: Completely accretive operators. Semigroup Theory and Evolution Equations. Lecture Notes in Pure and Applied Mathematics, pp. 41–75 (1989)Google Scholar
  3. 3.
    Crandall, M.G., Liggett, T.M.: Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93, 265–298 (1971)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Frank, T.D.: Nonlinear Fokker-Planck Equations. Springer, Berlin (2005)zbMATHGoogle Scholar
  5. 5.
    Frank, T.D., Daffertshofer, A.: \(h\)-Theorem for nonlinear Fokker-Planck equations related to generalized thermostatistics. Phys. A 295, 455–474 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jordan, R., Kinderlehrer, D., Otto, F.: The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29, 1–17 (1998)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Plastino, A.R., Plastino, A.: Phys. A 222, 347 (1995)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Octav Mayer Institute of Mathematics of the Romanian AcademyIasiRomania

Personalised recommendations