Boundary value problems | |
Analysis of the inverse problem in a time fractional parabolic equation with mixed boundary conditions | |
Ebru Ozbilge1  Ali Demir2  | |
[1] Department of Mathematics, Faculty of Science and Literature, Izmir University of Economics, Balcova, Izmir, Turkey;Department of Mathematics, Kocaeli University, Umuttepe, Turkey | |
关键词: Inverse Problem; Fractional Differential Equation; Parabolic Problem; Unknown Coefficient; Mixed Boundary Condition; | |
DOI : 10.1186/1687-2770-2014-134 | |
学科分类:数学(综合) | |
来源: SpringerOpen | |
【 摘 要 】
This article deals with the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficientk(x)in the linear time fractional parabolic equationDtαu(x,t)=(k(x)ux)x,0<α≤1, with mixed boundary conditionsu(0,t)=ψ0(t),ux(1,t)=ψ1(t). By defining the input-output mappingsΦ[⋅]:K→C1[0,T]andΨ[⋅]:K→C[0,T], the inverse problem is reduced to the problem of their invertibility. Hence the main purpose of this study is to investigate the distinguishability of the input-output mappingsΦ[⋅]andΨ[⋅]. This work shows that the input-output mappingsΦ[⋅]andΨ[⋅]have the distinguishability property. Moreover, the valuek(0)of the unknown diffusion coefficientk(x)atx=0can be determined explicitly by making use of measured output data (boundary observation)k(0)ux(0,t)=f(t), which brings greater restriction on the set of admissible coefficients. It is also shown that the measured output dataf(t)andh(t)can be determined analytically by a series representation, which implies that the input-output mappingsΦ[⋅]:K→C1[0,T]andΨ[⋅]:K→C[0,T]can be described explicitly.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201904025374798ZK.pdf | 280KB | download |