Existence and BV-regularity for neutron transport equation in nonconvex domain (Q2823011)
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scientific article; zbMATH DE number 6633209
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and BV-regularity for neutron transport equation in nonconvex domain |
scientific article; zbMATH DE number 6633209 |
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6 October 2016
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kinetic equations
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Boltzmann equation
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boundary conditions
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stochastic cycles
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existence and regularity of solutions
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Existence and BV-regularity for neutron transport equation in nonconvex domain (English)
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The paper addresses a linear three-dimensional kinetic equation, which models the transport of neutrons in the product of the coordinate and velocity spaces. The objective is to rigorously prove the existence and regularity of solutions over a long time interval. The main technical difficulty is handling the respective boundary conditions -- in particular, those in the coordinate subspace which correspond to a nonconvex shape of the spatial domain. The proof is based on the method of stochastic cycles, which was previously applied to produce rigorous results for the Boltzmann equation.
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