Lipschitz stability of an inverse problem for the Kawahara equation with damping

The aim of this paper is to establish a stability result regarding the inverse problem of retrieving the damping coefficient in Kawahara equation. We first establish an internal Carleman estimate for the linearized problem with the help of Dirichlet-Neumann type boundary conditions. Using the obtain...

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Published inAIMS mathematics Vol. 5; no. 5; pp. 4529 - 4545
Main Authors Anbu, Arivazhagan, Kumarasamy, Sakthivel, Balan Natesan, Barani
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
carleman estimate
inverse problems
kawahara equation
stability
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ISSN2473-6988
2473-6988
DOI10.3934/math.2020291

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Abstract The aim of this paper is to establish a stability result regarding the inverse problem of retrieving the damping coefficient in Kawahara equation. We first establish an internal Carleman estimate for the linearized problem with the help of Dirichlet-Neumann type boundary conditions. Using the obtained Carleman estimate and the regularity of solutions for the Kawahara equation, we prove the Lipschitz type stability and uniqueness of the considered inverse problems.
AbstractList The aim of this paper is to establish a stability result regarding the inverse problem of retrieving the damping coefficient in Kawahara equation. We first establish an internal Carleman estimate for the linearized problem with the help of Dirichlet-Neumann type boundary conditions. Using the obtained Carleman estimate and the regularity of solutions for the Kawahara equation, we prove the Lipschitz type stability and uniqueness of the considered inverse problems.
Author Anbu, Arivazhagan
Balan Natesan, Barani
Kumarasamy, Sakthivel
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Cites_doi 10.1143/JPSJ.33.260
10.1080/00036811.2012.716589
10.1051/cocv/2014059
10.1088/0266-5611/14/5/009
10.1007/BF00969507
10.1016/j.na.2015.01.015
10.1016/j.jmaa.2013.05.050
10.1016/j.jmaa.2011.07.003
10.1016/j.na.2019.03.016
10.3934/cpaa.2018088
10.1051/cocv/2009041
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CorporateAuthor 1 Department of Mathematics, Central University of Tamil Nadu, Thiruvarur 610 005, INDIA
2 Department of Mathematics, Indian Institute of Space Science and Technology (IIST), Trivandrum-695 547, INDIA
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Snippet The aim of this paper is to establish a stability result regarding the inverse problem of retrieving the damping coefficient in Kawahara equation. We first...
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SubjectTerms carleman estimate
inverse problems
kawahara equation
stability
Title Lipschitz stability of an inverse problem for the Kawahara equation with damping
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