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Existence of solutions of transport equations with nonlinear boundary conditions. (English) Zbl 0881.35115
The paper deals with transport equations, but with boundary condition different from the usual linear one. Instead, one introduces a new family of boundary conditions, which are generalization of the diffuse reflection law:
(i) The accomodation coefficient depends on the outgoing mass flux.
(ii) The probability density depends upon the outgoing trace.
The purpose of the paper is to prove the existence of some solution with the boundary condition (i) or (ii).
MSC:
35Q72 Other PDE from mechanics (MSC2000)
82C70 Transport processes in time-dependent statistical mechanics
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