Inverse scattering and inverse boundary value problems for the linear boltzmann equation

DOI10.1080/03605309608821207zbMath0857.35131OpenAlexW2150128110MaRDI QIDQ4887932

Mourad Choulli, Plamen D. Stefanov

Publication date: 9 March 1997

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

Full work available at URL: https://doi.org/10.1080/03605309608821207

zbMATH Keywords

Schrödinger operatorscattering operatorDirichlet-to-Neumann mapalbedo operatorlinear Boltzmann equation

Mathematics Subject Classification ID

Related Items (28)

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization ⋮ Unique Reconstruction of the Heat-Reflection Indices at Solid Interfaces ⋮ Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ Generalized stability estimates in inverse transport theory ⋮ Determining the collision kernel in the Boltzmann equation near the equilibrium ⋮ Numerical Reconstruction of Radiative Sources in an Absorbing and Nondiffusing Scattering Medium in Two Dimensions ⋮ Diffusive Optical Tomography in the Bayesian Framework ⋮ On diffusive scaling in acousto-optic imaging ⋮ Stability of stationary inverse transport equation in diffusion scaling ⋮ Parameter Reconstruction for General Transport Equation ⋮ Optical Tomography on Simple Riemannian Surfaces ⋮ Inverse problem for a free transport equation using Carleman estimates ⋮ Optical Tomography for Variable Refractive Index with Angularly Averaged Measurements ⋮ Stability of Inverse Transport Equation in Diffusion Scaling and Fokker--Planck Limit ⋮ Inverse transport calculations in optical imaging with subspace optimization algorithms ⋮ Inverse Problems for the Stationary Transport Equation in the Diffusion Scaling ⋮ Recovery of coefficients in the linear Boltzmann equation ⋮ A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium ⋮ Reconstruction of the Collision Kernel in the Nonlinear Boltzmann Equation ⋮ Unique Determination of Absorption Coefficients in a Semilinear Transport Equation ⋮ Uniqueness and non-uniqueness in inverse radiative transfer ⋮ Applications of kinetic tools to inverse transport problems ⋮ The structure of the fundamental solution of the time-independent transport equation ⋮ An inverse problem for the linear Boltzmann equation with a time-dependent coefficient ⋮ Angular Average of Time-Harmonic Transport Solutions ⋮ An inverse problem for the relativistic Boltzmann equation ⋮ Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography ⋮ Reconstructing the Thermal Phonon Transmission Coefficient at Solid Interfaces in the Phonon Transport Equation

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