Abstract
We are interested in non-standard transport equations where the description of the scattering events involves an additional variable''. We establish the well posedness and investigate the diffusion asymptotics of such models. While the questions we address are quite classical the analysis is original since the usual dissipative properties of collisional transport equations is broken by the introduction of the memory terms.
Highlights
This paper is devoted to the analysis of the following non-classical transport equation:
It has been shown that this model accurately describes experimental data for neutron transport in pebble-bed reactors [13]
The nomenclature of [8]) is the path length traveled by the particle since its previous interaction, or, equivalently, it can be thought of as the time elapsed since the previous interaction
Summary
This paper is devoted to the analysis of the following non-classical transport equation:. A model of similar type has been proposed for production systems [11] In this equation, Ψ(s, x, v) is the angular particle flux at point x into direction v. The probability that this particle interacts with the background medium is proportional to ds, and the proportionality constant depends on the density of the medium and on the particle’s energy This typically leads to an exponential attenuation law, i.e. the particle flux decreases as an exponential function of the path length (Beer-Lambert law). Dv is the normalized Lebesgue measure on SN−1, and σ(v, v ) = σ0(v · v ) In this case, we can define the mean scattering cosine μ0 v = v σ0(v · v ) dv , where μ0 is a constant independent of v.
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