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Nonlinear parabolic equations for measures


Authors: O. A. Manita and S. V. Shaposhnikov
Translated by: O. A. Manita
Original publication: Algebra i Analiz, tom 25 (2013), nomer 1.
Journal: St. Petersburg Math. J. 25 (2014), 43-62
MSC (2010): Primary 35K55
DOI: https://doi.org/10.1090/S1061-0022-2013-01279-9
Published electronically: November 20, 2013
MathSciNet review: 3113428
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Abstract: A new existence result is established for weak parabolic equations for probability measures. Sufficient conditions are given for the existence of local and global-in-time probability solutions of the Cauchy problem for such equations. Some conditions under which global-in-time solutions do not exist are indicated.


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Additional Information

O. A. Manita
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia
Email: oxana.manita@gmail.com

S. V. Shaposhnikov
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia
Email: starticle@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2013-01279-9
Keywords: Probability measures, nonlinear parabolic equations, transport equations, Vlasov equations, Fokker--Planck--Kolmogorov equations
Received by editor(s): February 12, 2012
Published electronically: November 20, 2013
Additional Notes: Supported by RFBR (grants nos. 10-01-00518-a, 11-01-00348-a, 11-01-12018-ofi-m-2011, 12-01-92103-JFa), the Russian Federation President grant MK-3674.2011.1, and by the SFB 701 at the Bielefeld University.
Article copyright: © Copyright 2013 American Mathematical Society