Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit. (English) Zbl 1412.82019
Two different scalings of the Boltzmann transport equation for photons are considered: the diffusive and the Fokker-Planck ones. The inverse problem for the corresponding equations is studied, which consists in the reconstruction of the scattering and the absorption coefficients starting from boundary measurements. In particular, the authors assess how the error in the measurements is amplified or suppressed in the reconstruction. As regards the first limit, the authors show that the distinguishability coefficient, both for the absorption and the scattering coefficients, is bad for small Knudsen number. In the second limit it is shown that a full recovery of the scattering coefficient is less possible. In both cases, the linearization approach is used.
Reviewer: Giovanni Mascali (Arcavacata di Rende)
MSC:
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35L99 | Hyperbolic equations and hyperbolic systems |
| 35K99 | Parabolic equations and parabolic systems |
| 82C70 | Transport processes in time-dependent statistical mechanics |
| 35Q20 | Boltzmann equations |
Keywords:
transport equation; diffusion limit; Fokker-Planck limit; stability; inverse problem; absorption and scattering coefficientsReferences:
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