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

Arivazhagan Anbu; Sakthivel Kumarasamy; Barani Balan Natesan; Arivazhagan Anbu; Sakthivel Kumarasamy; Barani Balan Natesan

doi:10.3934/math.2020291

AIMS Mathematics

2020, Volume 5, Issue 5: 4529-4545. doi: 10.3934/math.2020291

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Research article

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

Received: 31 December 2019 Accepted: 08 May 2020 Published: 21 May 2020
MSC : 35K05, 35R30, 35Q53

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.
- stability,
- inverse problems,
- Kawahara equation,
- Carleman estimate
Citation: Arivazhagan Anbu, Sakthivel Kumarasamy, Barani Balan Natesan. Lipschitz stability of an inverse problem for the Kawahara equation with damping[J]. AIMS Mathematics, 2020, 5(5): 4529-4545. doi: 10.3934/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.

References

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