On uniqueness of solutions to nonlinear Fokker–Planck–Kolmogorov equations

We study uniqueness of families of probability measures solving the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equation with unbounded coefficients. Sufficient conditions for uniqueness are indicated and examples of non-uniqueness are constructed.

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Bibliographische Detailangaben
Veröffentlicht in:	Nonlinear analysis 2015-11, Vol.128, p.199-226
Hauptverfasser:	Manita, Oxana A., Romanov, Maxim S., Shaposhnikov, Stanislav V.
Format:	Artikel
Sprache:	eng
Schlagworte:	Cauchy problem Construction Mathematical analysis McKean–Vlasov equation Nonlinearity Nonlinear Fokker–Planck–Kolmogorov equation Uniqueness Uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations
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Beschreibung
Zusammenfassung:	We study uniqueness of families of probability measures solving the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equation with unbounded coefficients. Sufficient conditions for uniqueness are indicated and examples of non-uniqueness are constructed.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2015.08.008