Abstract
In this paper, we consider a seventh-order generalized Korteweg–de Vries (GKdV) equation and study the boundary stability results concerning the inverse problem of recovering a space-dependent source term. We establish a new boundary Carleman estimate for the seventh-order linear operator with the Dirichlet–Neumann type boundary conditions. Using this crucial estimate along with regularity result of the nonlinear GKdV equation, we establish a Lipschitz stability estimate of GKdV equation.
Funding source: National Board for Higher Mathematics
Award Identifier / Grant number: 2/48(2)/2015/NBHM(R.P.)/R&D-II/14183
Funding statement: The third author is supported by National Board for Higher Mathematics (NBHM), Department of Atomic Energy, India through research project grant (Project Grant No. 2/48(2)/2015/NBHM(R.P.)/R&D-II/14183).
Acknowledgements
The authors thank the anonymous referees for their careful reading and valuable comments which helped to improve the quality of the manuscript.
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