Uniqueness and continuous dependence for a multidimensional hyperbolic inverse problem

DOI10.1080/03605308508820391zbMath0574.35078OpenAlexW2052688416MaRDI QIDQ3693960

Paul E. Sacks, William W. Symes

Publication date: 1985

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308508820391

zbMATH Keywords

optimizationLaplace transformSobolev spaceinverse problemuniquenessimpulse responsecontinuous dependenceacoustic mediumvibratory state

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Laplace transform (44A10) Second-order hyperbolic equations (35L10)

Related Items (12)

Global recovery of a time-dependent coefficient for the wave equation from a single measurement ⋮ Time-domain optimization of input signals for distributed-parameter systems identification ⋮ On the sensitivity of solutions of hyperbolic ⋮ Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations ⋮ Uniqueness for an inverse problem for the wave equation ⋮ Uniqueness for a hyperbolic inverse problem with angular control on the coefficients ⋮ An inverse problem for the wave equation with source and receiver at distinct points ⋮ The fixed angle scattering problem and wave equation inverse problems with two measurements ⋮ A meshfree method for inverse wave propagation using collocation and radial basis functions ⋮ On the uniquencess of a multidimensional hyperbolic inverse problem ⋮ Linearization ill-posedness for 2. 5-D wave equation inversion model ⋮ On continuous dependence for an inverse initial boundary value problem for the wave equation

Cites Work

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• Impedance profile inversion via the first transport equation
• The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
• About the stability of the inverse problem in 1-D wave equations application to the interpretation of seismic profiles
• The One-Dimensional Inverse Problem of Reflection Seismology
• On the Relation between Coefficient and Boundary Values for Solutions of Webster’s Horn Equation
• Linearization Stability for an Inverse Problem in Several-Dimensional Wave Propagation
• Scattering techniques for a one dimensional inverse problem in geophysics
• Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium
• Least Squares Methods for Ill-Posed Problems with a Prescribed Bound

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