ON A NONLINEAR STATIONARY PROBLEM ARISING IN TRANSPORT-THEORY

In this article a nonlinear one-dimensional stationary transport equat ion with general boundary conditions is considered where an abstract b oundary operator relates the incoming and the outgoing fluxes. Existen ce results are proved in the case where the collision operator is of t he Hammerstein type. In particular, it is shown that these results rem ain valid for multidimensional geometry with vacuum boundary condition s. 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 bound ary conditions. (C) 1996 American Institute of Physics.