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Coupling of transport and diffusion models in linear transport theory. (English) Zbl 0995.45008

The paper concerns the coupling of two models for the propagation of particles in scattering media. The first one is a linear transport equation of Boltzmann type posed in the phase space and the second one is a diffusion equation posed in the physical space. The coupling of these models accounts for diffusive and non-diffusive regions and the interface separating the models is chosen such that the diffusive regime holds in its vicinity to avoid the calculation of boundary or interface layers. The coupled problem is analyzed theoretically and numerically.

MSC:

45K05 Integro-partial differential equations
92C55 Biomedical imaging and signal processing
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
82C70 Transport processes in time-dependent statistical mechanics
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