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On regularity of solutions for certain linear Boltzmann transport equations
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The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their collision terms. Hyper-singular integrals can be approximated by partial differential operators together with partial integral operators which leads to an approximation under consideration. This type of approximation is applied, for example in the dose calculation of radiation therapy. The related transport problem is a characteristic initial inflow boundary value problem. Regularity results of solutions are verified utilizing the scales of relevant anisotropic Sobolev spaces.
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On existence of spatially regular strong solutions for a class of transport equations
For linear Boltzmann transport problems whose data vanish on the inflow and characteristic boundary parts, strong solutions exist with arbitrary spatial Sobolev regularity, including with a continuous slowing-down ene...
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