A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
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Michael V. Klibanov
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Vladimir G. Romanov
Abstract
A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problem with the initial condition being the delta function concentrated at a single plane (i.e. the plane wave). A certain associated operator is written in finite differences with respect to two out of three spatial variables, i.e. “partial finite differences”. The grid step size is bounded from below by a fixed number. A Carleman estimate is applied to obtain, for the first time, a Hölder stability estimate for this problem. Another new result is an estimate from below the amplitude of the first term of the expansion of the solution of the forward problem near the characteristic wedge.
Funding source: Siberian Branch, Russian Academy of Sciences
Award Identifier / Grant number: FWNF-2022-0009
Funding statement: The work of V. G. Romanov was supported by a grant from the Siberian Branch of the Russian Academy of Sciences, project number FWNF-2022-0009.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Stability of determination of Riemann surface from its DN-map in terms of holomorphic immersions
- Reconstruction of acoustic sources from multi-frequency phaseless far-field data
- Block Toeplitz Inner-Bordering method for the Gelfand–Levitan–Marchenko equations associated with the Zakharov–Shabat system
- The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method
- A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
- A primal-dual approach for the Robin inverse problem in a nonlinear elliptic equation: The case of the 𝐿1 − 𝐿2 cost functional
- A range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt–Kaczmarz method for solving systems of non-linear ill-posed equations: Application to EIT-CEM with real data
- C-regularized solutions of ill-posed problems defined by strong strip-type operators
Artikel in diesem Heft
- Frontmatter
- Stability of determination of Riemann surface from its DN-map in terms of holomorphic immersions
- Reconstruction of acoustic sources from multi-frequency phaseless far-field data
- Block Toeplitz Inner-Bordering method for the Gelfand–Levitan–Marchenko equations associated with the Zakharov–Shabat system
- The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method
- A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
- A primal-dual approach for the Robin inverse problem in a nonlinear elliptic equation: The case of the 𝐿1 − 𝐿2 cost functional
- A range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg–Marquardt–Kaczmarz method for solving systems of non-linear ill-posed equations: Application to EIT-CEM with real data
- C-regularized solutions of ill-posed problems defined by strong strip-type operators
