Existence Theorems for the Linear, Space-inhomogeneous Transport Equation |
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Authors: | PETTERSSON ROLF |
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Institution: |
Department of Mathematics, Chalmers University of Technology and the University of G?teborg S-41296 G?teborg, Sweden
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Abstract: | This paper studies existence problems in L1 for the linear,space-inhomogeneous Boltzmann equation with periodic or (perfectly)absorbing boundary conditions under realistic assumptions onthe cross-sections. By an iteration technique, solutions arefirst constructed to an integral equation variant of the transportequation in the case of bounded impact parameters and an L1type of cross-sections. They are then used to study the existenceof solutions of a measure form of the transport equation inthe case of unbounded impact parameters. These solutions conservemass. Estimates of their higher moments are also given. In particularthe results hold for inverse kth-power forces with 3 < k 5. |
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