Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials

DOI10.1007/BF01215158zbMath0653.35049MaRDI QIDQ1107731

Plamen D. Stefanov

Publication date: 1989

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174072

zbMATH Keywords

polynomial growthwave equationplane wavesuniquenesssingularityinverse scattering problemscattering kerneltime dependent potential

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Second-order hyperbolic equations (35L10)

Related Items (41)

Unique determination of a time-dependent potential for wave equations from partial data ⋮ Global recovery of a time-dependent coefficient for the wave equation from a single measurement ⋮ RECOVERY OF ZEROTH ORDER COEFFICIENTS IN NON-LINEAR WAVE EQUATIONS ⋮ Linearized boundary control method for an acoustic inverse boundary value problem ⋮ An inverse hyperbolic problem with many boundary measurements ⋮ The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds ⋮ Stable Determination of Time-Dependent Scalar Potential from Boundary Measurements in a Periodic Quantum Waveguide ⋮ Lorentzian Calderón problem under curvature bounds ⋮ Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ Stability estimate for a hyperbolic inverse problem with time-dependent coefficient ⋮ Stable Determination of X-Ray Transforms of Time Dependent Potentials from Partial Boundary Data ⋮ Support theorem for the light-ray transform of vector fields on Minkowski spaces ⋮ Determination of singular time-dependent coefficients for wave equations from full and partial data ⋮ Inverse problems for general second order hyperbolic equations with time-dependent coefficients ⋮ Support theorems for the light ray transform on analytic Lorentzian manifolds ⋮ The light ray transform on Lorentzian manifolds ⋮ Stability estimate for an inverse problem for the Schrödinger equation in a magnetic field with time-dependent coefficient ⋮ Inverse problems for real principal type operators ⋮ Stability in the determination of a time-dependent coefficient for wave equations from partial data ⋮ Reconstruction of a time-dependent potential from wave measurements ⋮ An inverse problem for the wave equation ⋮ Hölder Stably Determining the Time-Dependent Electromagnetic Potential of the Schrödinger Equation ⋮ Inverse scattering problem for moving obstacles ⋮ An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials ⋮ Travel time tomography in stationary spacetimes ⋮ X-ray transforms in pseudo-Riemannian geometry ⋮ Stable determination outside a cloaking region of two time-dependent coefficients in an hyperbolic equation from Dirichlet to Neumann map ⋮ Stable recovery of time dependent coefficient from arbitrary measurements for wave equation ⋮ Inverse Hyperbolic Problems with Time-Dependent Coefficients ⋮ The light ray transform in stationary and static Lorentzian geometries ⋮ Inverse problem for the Yang-Mills equations ⋮ Inverse scattering and stability for the biharmonic operator ⋮ Recovery of Nonsmooth Coefficients Appearing in Anisotropic Wave Equations ⋮ A partial data inverse problem for the convection-diffusion equation ⋮ Low regularity ray tracing for wave equations with Gaussian beams ⋮ A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem ⋮ Recovery of Time-Dependent Damping Coefficients and Potentials Appearing in Wave Equations from Partial Data ⋮ Recovery of time-dependent coefficients from boundary data for hyperbolic equations ⋮ Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations ⋮ Inverse problem for Einstein-scalar field equations ⋮ Property C and an inverse problem for a hyperbolic equation

Cites Work

• The leading singularity of a wave reflected by a moving boundary
• Inverse scattering problem for the wave equation with time-dependent potential
• The Radon transform
• On the decay of local energy for wave equations with time-dependent potentials
• A formulation for higher dimensional inverse problems for the wave equation
• Scattering of waves by periodically moving bodies
• Some properties of the scattering amplitude and the inverse scattering problem
• Scattering of plane waves by a moving obstacle
• The acoustic equation with an indefinite energy form and the Schrödinger equation
• A rigorous derivation of the ‘‘miracle’’ identity of three-dimensional inverse scattering
• Uniqueness of the inverse scattering problem for the wave equation with a potential depending on time
• The Newton-Marchenko equation for time-dependent potentials
• Scattering properties of wave equations with time-dependent potentials
• Variational principles for inverse scattering
• Time dependent approach to the inverse scattering problem for wave equations with time dependent coefficients
• Eigenfunction expansions associated with the Schrödinger operator with a complex potential and the scattering inverse problem
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