Analysis of the inverse problem in a time fractional parabolic equation with mixed boundary conditions
1 Department of Mathematics, Faculty of Science and Literature, Izmir University of Economics, Sakarya Caddesi, No. 156, Balcova, Izmir, 35330, Turkey
2 Department of Mathematics, Kocaeli University, Umuttepe, Izmit, Kocaeli, 41380, Turkey
Boundary Value Problems 2014, 2014:134 doi:10.1186/1687-2770-2014-134Published: 27 May 2014
This article deals with the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient in the linear time fractional parabolic equation , , with mixed boundary conditions , . By defining the input-output mappings and , 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 mappings and . This work shows that the input-output mappings and have the distinguishability property. Moreover, the value of the unknown diffusion coefficient at can be determined explicitly by making use of measured output data (boundary observation) , which brings greater restriction on the set of admissible coefficients. It is also shown that the measured output data and can be determined analytically by a series representation, which implies that the input-output mappings and can be described explicitly.