Uniqueness and counterexamples in some inverse source problems

M. Slodička*, B. Tomas Johansson

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)56-61
Number of pages6
JournalApplied Mathematics Letters
Volume58
Early online date15 Feb 2016
DOIs
Publication statusPublished - Aug 2016

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

  • heat equation
  • inverse source problem

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