Published January 1, 2013
| Version v1
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An analysis of inverse source problems with final time measured output data for the heat conduction equation: A semigroup approach
Creators
- 1. Izmir Univ, Dept Math & Comp Sci, TR-35350 Izmir, Turkey
- 2. Univ Ghent, Dept Math Anal, B-9000 Ghent, Belgium
Description
This paper presents a semigroup approach for inverse source problems for the abstract heat equation U-t = Au + F, when the measured output data is given in the form the final overdetermination u(T)(x) := u(x, T). A representation formula for a solution of the inverse source problem is proposed. This representation shows a non-uniqueness structure of the inverse problem solution, and also permits one to derive a sufficient condition for uniqueness. Some examples related to identifying the unknown spacewise and time-dependent heat sources f (x) and h(t) of the heat equation 14, = u(t) + f (x)h(t), from the final overdetermination or from a single point time measurement are presented. (C) 2012 Elsevier Ltd. All rights reserved.
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