Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations

DOI10.1093/imrn/rnx263zbMath1459.35398arXiv1606.07243OpenAlexW2963699209WikidataQ115272892 ScholiaQ115272892MaRDI QIDQ5855186

Lauri Oksanen, Yavar Kian

Publication date: 15 March 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07243

zbMATH Keywords

Calderón problemdetermining a time-dependent potential

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Inverse problems for PDEs (35R30) PDEs on manifolds (35R01)

Related Items (17)

Global recovery of a time-dependent coefficient for the wave equation from a single measurement ⋮ The light ray transform on Lorentzian manifolds ⋮ Determining a nonlinear hyperbolic system with unknown sources and nonlinearity ⋮ RECOVERY OF NON-COMPACTLY SUPPORTED COEFFICIENTS OF ELLIPTIC EQUATIONS ON AN INFINITE WAVEGUIDE ⋮ On the scientific work of Victor Isakov ⋮ Hölder Stably Determining the Time-Dependent Electromagnetic Potential of the Schrödinger Equation ⋮ X-ray transforms in pseudo-Riemannian geometry ⋮ The light ray transform in stationary and static Lorentzian geometries ⋮ Recovery of Nonsmooth Coefficients Appearing in Anisotropic Wave Equations ⋮ A partial data inverse problem for the convection-diffusion equation ⋮ A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem ⋮ Counterexamples to inverse problems for the wave equation ⋮ Recovery of time-dependent coefficients from boundary data for hyperbolic equations ⋮ Application of the boundary control method to partial data Borg-Levinson inverse spectral problem ⋮ Stability estimate for a partial data inverse problem for the convection-diffusion equation ⋮ On the determination of nonlinear terms appearing in semilinear hyperbolic equations ⋮ Determining the time-dependent matrix potential in a wave equation from partial boundary data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Calderón problem in transversally anisotropic geometries
• Stability of the determination of a coefficient for wave equations in an infinite waveguide
• Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map
• Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem
• An introduction to inverse elliptic and parabolic problems
• Completeness of products of solutions and some inverse problems for PDE
• Property C and an inverse problem for a hyperbolic equation
• Limiting Carleman weights and anisotropic inverse problems
• Stability in the determination of a time-dependent coefficient for wave equations from partial data
• An inverse problem for the wave equation
• The X-ray transform for a generic family of curves and weights
• Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem
• Non-unicité du problème de Cauchy
• Non homogeneous boundary value problems for second order hyperbolic operators
• Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials
• Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media
• On uniqueness in inverse problems for semilinear parabolic equations
• Inverse problems for the connection Laplacian
• Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. application to the determination of a nonlinear term
• A non uniqueness result for operators of principal type
• Stability of the Calderón problem in admissible geometries
• Unique determination of a time-dependent potential for wave equations from partial data
• Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets
• The Calderón problem with partial data on manifolds and applications
• The Calderón problem with partial data
• Recovery of Time-Dependent Damping Coefficients and Potentials Appearing in Wave Equations from Partial Data
• Stable Determination of X-Ray Transforms of Time Dependent Potentials from Partial Boundary Data
• Support theorems for the light ray transform on analytic Lorentzian manifolds
• Lipschitz stability for a hyperbolic inverse problem by finite local boundary data
• A Lipschitz stable reconstruction formula for the inverse problem for the wave equation
• Stability estimate for a hyperbolic inverse problem with time-dependent coefficient
• To the reconstruction of a riemannian manifold via its spectral data (Bc–Method)
• RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA
• Calderón problem for connections
• Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theorem
• Stable Determination of a Simple Metric, a Covector Field and a Potential from the Hyperbolic Dirichlet-to-Neumann Map
• Recent progress in the boundary control method
• Inverse Hyperbolic Problems with Time-Dependent Coefficients
• Determination of time-dependent coefficients for a hyperbolic inverse problem

This page was built for publication: Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations