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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Bibliographic Details
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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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020291