Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations

doi:10.1515/jiip-2014-0022

	Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
	Feng, Pengbin 1; Karimov, Erkinjon T.2
刊名	JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
	2015-08-01
卷号	23 期号:4 页码:339-353
关键词	Inverse source problem Caputo fractional derivative mixed-type equation orthonormal system of eigenfunctions
ISSN号	0928-0219
DOI	10.1515/jiip-2014-0022
英文摘要	In the present paper we consider an inverse source problem for a time-fractional mixed parabolic-hyperbolic equation with Caputo derivatives. In the case when the hyperbolic part of the considered mixed-type equation is the wave equation, the uniqueness of the source and the solution are strongly influenced by the initial time and the problem is generally ill-posed. However, when the hyperbolic part is time-fractional, the problem is well-posed if the end time is large. Our method relies on the orthonormal system of eigenfunctions of the operator with respect to the space variables. Finally, we prove uniqueness and stability of certain weak solutions for the problems under consideration.
WOS研究方向	Mathematics
语种	英语
出版者	WALTER DE GRUYTER GMBH
WOS记录号	WOS:000358986200004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/20503]
专题	中国科学院数学与系统科学研究院
通讯作者	Feng, Pengbin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Natl Univ Uzbekistan, Inst Math, Tashkent 100125, Uzbekistan
推荐引用方式 GB/T 7714	Feng, Pengbin,Karimov, Erkinjon T.. Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations[J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS,2015,23(4):339-353.
APA	Feng, Pengbin,&Karimov, Erkinjon T..(2015).Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations.JOURNAL OF INVERSE AND ILL-POSED PROBLEMS,23(4),339-353.
MLA	Feng, Pengbin,et al."Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations".JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 23.4(2015):339-353.