Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations

doi:10.1016/j.jfa.2021.108926

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	Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations
	Barbu, Viorel 1; Roeckner, Michael 2,3
	2021-04-01
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	280 期号:7 页码:35
摘要	One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker-Planck equation (FPE) u(t) - Delta(beta(u)) + div(D(x)b(u)u) = 0, t >= 0, x is an element of R-d, d not equal 2, u(0, .) = u(0), in R-d, where u(0) is an element of L-1 (R-d ), beta is an element of C-2 (R) is a nondecreasing function, b is an element of C-1, bounded, b >= 0, D is an element of L-infinity (R-d; R-d) with div D is an element of (L-2+L infinity)(R-d), and (div D)(-) is an element of L-infinity (R-d), beta strictly increasing, if b is not constant. Moreover, t -> u(t, u(0)) is a semigroup of contractions in L-1 (R-d), which leaves invariant the set of probability density functions in R-d. If div D >= 0, beta'(r) >= a vertical bar r vertical bar(alpha-)(1) and vertical bar beta(r)vertical bar <= Cr-alpha, alpha >= 1, d >= 3, then vertical bar u(t)vertical bar L-infinity <= Ct(-d/d+(alpha-1)d) vertical bar u(0)vertical bar(2/2+(m-1d)), t > 0, and if D is an element of L-2 (R-d;R-d) the existence extends to initial data u(0) in the space M-b of bounded measures in R-d. As a consequence for arbitrary initial laws, we obtain weak solutions to a class of McKean-Vlasov SDEs with coefficients which have singular dependence on the time marginal laws. (C) 2021 Elsevier Inc. All rights reserved.
关键词	Fokker-Planck equation m-accretive Measure as initial data McKean-Vlasov stochastic differential equation
DOI	10.1016/j.jfa.2021.108926
收录类别	SCI
语种	英语
资助项目	DFG[CRC 1283]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000615710700020
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58207
专题	中国科学院数学与系统科学研究院
通讯作者	Barbu, Viorel
作者单位	1.Romanian Acad, Octav Mayer Inst Math, Iasi, Romania 2.Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Barbu, Viorel,Roeckner, Michael. Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2021,280(7):35.
APA	Barbu, Viorel,&Roeckner, Michael.(2021).Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations.JOURNAL OF FUNCTIONAL ANALYSIS,280(7),35.
MLA	Barbu, Viorel,et al."Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations".JOURNAL OF FUNCTIONAL ANALYSIS 280.7(2021):35.