Uniqueness and counterexamples in some inverse source problems


Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.

Publication DOI: https://doi.org/10.1016/j.aml.2016.02.001
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: heat equation ,inverse source problem,Applied Mathematics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2016-08
Published Online Date: 2016-02-15
Accepted Date: 2016-02-02
Submitted Date: 2015-11-19
Authors: Slodička, M.
Johansson, B. Tomas ( 0000-0001-9066-7922)

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