Abstract
In this article a nonlinear one-dimensional stationary transport equation with general boundary conditions is considered where an abstract boundary operator relates the incoming and the outgoing fluxes. Existence results are proved in the case where the collision operator is of the Hammerstein type. In particular, it is shown that these results remain valid for multidimensional geometry with vacuum boundary conditions. Sufficient conditions are given in terms of collision frequency and scattering kernel assuring the existence and uniqueness of solutions. The article ends with the discussion of the case of multiplying boundary conditions.
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