Uniqueness and counterexamples in some inverse source problems

M. Slodička; B. Tomas Johansson

doi:10.1016/j.aml.2016.02.001

Uniqueness and counterexamples in some inverse source problems

M. Slodička^*, B. Tomas Johansson

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	56-61
Number of pages	6
Journal	Applied Mathematics Letters
Volume	58
Early online date	15 Feb 2016
DOIs	https://doi.org/10.1016/j.aml.2016.02.001
Publication status	Published - Aug 2016

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Keywords

heat equation
inverse source problem

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10.1016/j.aml.2016.02.001

Uniqueness and counterexamples in some inverse source problems
© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 203 KBLicence: CC BY-NC-ND 3.0

Cite this

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title = "Uniqueness and counterexamples in some inverse source problems",

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.",

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author = "M. Slodi{\v c}ka and Johansson, {B. Tomas}",

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AU - Slodička, M.

AU - Johansson, B. Tomas

PY - 2016/8

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N2 - 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.

AB - 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.

KW - heat equation

KW - inverse source problem

UR - http://www.scopus.com/inward/record.url?scp=84959378550&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2016.02.001

DO - 10.1016/j.aml.2016.02.001

M3 - Article

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VL - 58

SP - 56

EP - 61

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Uniqueness and counterexamples in some inverse source problems

Abstract

Bibliographical note

Keywords

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