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

Autor:	Feng, Pengbin, Karimov, E. T.
Rok vydání:	2014
Předmět:	Mathematics - Analysis of PDEs 35R30
Zdroj:	J.Inverse Ill-Posed Probl.2015;23(4),339-353
Druh dokumentu:	Working Paper
Popis:	In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the uniqueness of source and solution are strongly influenced by initial time and generally is ill-posed. However, when the hyperbolic part is time fractional, the problem is well posed if end time is large. Our method relies on the orthonormal system of eigenfunctions of the operator with respect to space variable. We proved the uniqueness and stability of certain weak solutions for considered problems. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1401.6868 Zobrazit plný text záznamu View this record from Arxiv