Applied mathematics of transport theory: Final report, December 1, 1983-March 31, 1987

This is the final report for the subject grant. We have carried out a program of research in various areas of applied mathematics related to transport problems in kinetic theory. The term transport refers to physical problems in which the streaming aspects of the transported quantity dominate the collisional aspects, as when the mean free path in the flow exceeds the impact radius. Our work has largely been devoted to developing the theory of transport equations in an abstract setting, in order to treat systematically the large number of kinetic equations and to expand the range of equations subject to analysis, and preliminary to the study of related nonlinear systems. At the same time we have treated certain concrete models of particular physical interest, both from an analytic and from a computational point of view. We indicate below specific references to these developments.