Steady States of Fokker-Planck Equations: II. Non-existence

doi:10.1007/s10884-015-9470-x

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	Steady States of Fokker-Planck Equations: II. Non-existence
	Huang, Wen 1,2; Ji, Min3 ; Liu, Zhenxin 4,6; Yi, Yingfei 5,6,7
	2015-12-01
发表期刊	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN	1040-7294
卷号	27 期号:3-4 页码:743-762
摘要	This is the second paper in a series concerning the study of steady states, including stationary solutions and measures, of a Fokker-Planck equation in a general domain in with drift term and diffusion term for any . In this paper, we obtain some non-existence results of stationary measures under conditions involving anti-Lyapunov type of functions associated with the stationary Fokker-Planck equation. When combined with the existence results showed in part I of the series (Huang et al. in J. Dyn Differ Equ) contained in the same volume, not only will these results yield necessary and sufficient conditions for the existence of stationary measures, but also they provide a useful tool for one to study noise perturbations of systems of ordinary differential equations, especially with respect to problems of stochastic bifurcations, as demonstrated in some examples contained in this paper. Our analysis is based on the level set method, in particular the integral identity, and measure estimates contained in our work (Huang et al. in Ann Probab 43:1712-1730, 2015).
关键词	Fokker-Planck equation Non-existence Stationary solution Stationary measure Level set method
DOI	10.1007/s10884-015-9470-x
语种	英语
资助项目	NSFC[11225105] ; NSFC[11431012] ; NSFC[11271151] ; NSFC Innovation Grant[10421101] ; startup fund of Dalian University of Technology ; NSF[DMS0708331] ; NSF[DMS1109201] ; NSERC[1257749] ; University of Alberta ; Jilin University
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000366644300017
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21527
专题	数学所
通讯作者	Ji, Min
作者单位	1.Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China 2.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 4.Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China 5.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 6.Jilin Univ, Sch Math, Changchun 130012, Peoples R China 7.Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
推荐引用方式 GB/T 7714	Huang, Wen,Ji, Min,Liu, Zhenxin,et al. Steady States of Fokker-Planck Equations: II. Non-existence[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2015,27(3-4):743-762.
APA	Huang, Wen,Ji, Min,Liu, Zhenxin,&Yi, Yingfei.(2015).Steady States of Fokker-Planck Equations: II. Non-existence.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,27(3-4),743-762.
MLA	Huang, Wen,et al."Steady States of Fokker-Planck Equations: II. Non-existence".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 27.3-4(2015):743-762.