AIMS Mathematics, 2020, 5(5): 4529-4545. doi: 10.3934/math.2020291

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

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

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.
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