Existence and uniqueness for nonlinear boundary value problems in kinetic theory |
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| Authors: | Carlo Cercignani Andrzej Palczewski |
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| Affiliation: | (1) Dipartimento di Matematica del Politecnico di Milano, Milan, Italy;(2) Department of Mathematics, University of Warsaw, Warsaw, Poland |
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| Abstract: | A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies. |
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| Keywords: | Boltzmann equation boundary value problem kinetic theory |
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