Mathematical Sciences: Applied Mathematics of Transport Theory

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This research will study initial-boundary value problems arising in kinetic reference theory, especially equations of Boltzmann, Enskog, B.G.K., and various modifications. Existence, uniqueness, regularity and asymptotic properties are sought. Professors Zweifel and Greenberg will continue the development of perturbation theory for co-bisemigroups, especially in the Banach space setting, and the related Wiener-Hopf factorization theory. Explicit application to certain linearized transport equations is also proposed. Numerical simulation applied to the Vlasov- Poisson system, to mumesonic transport, and to scaling properties of dynamical systems is intended. These studies are foundations for application in areas such as radiative transfer, neutron transport, and rarefied gas dynamics.