Abstract
An abstract differential equation with “partial range” boundary conditions, modelling a variety of plane-symmetric stationary transport phenomena, is studied in Hilbert space. The collision operator is assumed to be a positive compact perturbation of the identity. A complete existence and uniqueness theory for the abstract equation is presented and two examples from rarefied gas dynamics are detailed.
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Work supported in part by D.O.E. grant No. DE-AS05 80ER10711 and N.S.F. grant No. DMS-8312451.
The research was carried out while the author was visiting the Department of Physics and Astronomy of the Free University of Amsterdam, The Netherlands.
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Greenberg, W., van der Mee, C. & Walus, W. Strong solutions of stationary equations in abstract kinetic theory. Integr equ oper theory 11, 186–204 (1988). https://doi.org/10.1007/BF01272118
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DOI: https://doi.org/10.1007/BF01272118