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

doi:10.1515/jiip-2014-0022

CSpace

	Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
	Feng, Pengbin 1; Karimov, Erkinjon T.2
	2015-08-01
发表期刊	JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
ISSN	0928-0219
卷号	23 期号:4 页码:339-353
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.
关键词	Inverse source problem Caputo fractional derivative mixed-type equation orthonormal system of eigenfunctions
DOI	10.1515/jiip-2014-0022
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000358986200004
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20504
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.