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International Conference on Stochastic Partial Differential Equations and Related Fields

SPDERF 2016: Stochastic Partial Differential Equations and Related Fields pp 367–379Cite as

Nonlinear Fokker–Planck–Kolmogorov Equations for Measures

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 229))

Abstract

Existence and uniqueness of solutions of the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for measures are investigated. We consider the difficult case when the diffusion matrix depends on the solution. Moreover we give a short survey of the known results connected with these problems.

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Acknowledgements

The author is grateful to Prof. V.I. Bogachev and Prof. M. Röckner for fruitful discussions and valuable remarks. The work was supported by the President Grant MD-207.2017.1, the RFBR grant 17-01-00622, the Simons Foundation, and the SFB 1283 at Bielefeld University.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Stanislav V. Shaposhnikov

  2. National Research University Higher School of Economics, Moscow, Russia

    Stanislav V. Shaposhnikov

  3. St.-Tikhon’s Orthodox Humanitarian University, Moscow, Russia

    Stanislav V. Shaposhnikov

Authors
  1. Stanislav V. Shaposhnikov
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Correspondence to Stanislav V. Shaposhnikov .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Andreas Eberle

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  3. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Walter Hoh

  4. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Moritz Kassmann

  5. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Wilhelm Stannat

  6. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

    Gerald Trutnau

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Shaposhnikov, S.V. (2018). Nonlinear Fokker–Planck–Kolmogorov Equations for Measures. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_24

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