Stability for a Formally Determined Inverse Problem for a Hyperbolic PDE with Space and Time Dependent Coefficients

DOI10.1137/21M1400596zbMath1482.35275arXiv2010.11726OpenAlexW3093765998WikidataQ115525521 ScholiaQ115525521MaRDI QIDQ5018859

Rakesh, Venkateswaran P. Krishnan, Soumen Senapati

Publication date: 24 December 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.11726

zbMATH Keywords

stability estimateshyperbolic inverse problemBukhgeim-Klibanov methodrecovery of first-order and zeroth-order coefficientsspace and time dependent coefficients

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Inverse problems for PDEs (35R30) A priori estimates in context of PDEs (35B45)

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Fixed Angle Inverse Scattering for Sound Speeds Close to Constant, Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition, Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients

Cites Work

• Unnamed Item
• Stable determination outside a cloaking region of two time-dependent coefficients in an hyperbolic equation from Dirichlet to Neumann map
• A global uniqueness theorem for an inverse boundary value problem
• Completeness of products of solutions and some inverse problems for PDE
• Property C and an inverse problem for a hyperbolic equation
• Inverse scattering problem for the wave equation with time-dependent potential
• An inverse problem for the wave equation
• Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map
• Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media
• The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds
• Inverse problems for general second order hyperbolic equations with time-dependent coefficients
• An inverse problem for the wave equation with one measurement and the pseudorandom source
• Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets
• An inverse problem of finding two time-dependent coefficients in second order hyperbolic equations from Dirichlet to Neumann map
• Recovery of Time-Dependent Damping Coefficients and Potentials Appearing in Wave Equations from Partial Data
• Boundary Control Method in Dynamical Inverse Problems — An Introductory Course
• Stability estimate for the relativistic Schrödinger equation with time-dependent vector potentials
• Stability estimate for a hyperbolic inverse problem with time-dependent coefficient
• Uniqueness for an inverse problem for the wave equation
• Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
• Hölder Stably Determining the Time-Dependent Electromagnetic Potential of the Schrödinger Equation
• Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
• An inverse problem for the relativistic Schrödinger equation with partial boundary data
• Stability estimates for the relativistic Schrödinger equation from partial boundary data
• Uniqueness for the inverse backscattering problem for angularly controlled potentials
• The fixed angle scattering problem and wave equation inverse problems with two measurements
• Recent progress in the boundary control method
• Inverse Hyperbolic Problems with Time-Dependent Coefficients
• Determination of time-dependent coefficients for a hyperbolic inverse problem