Mathematical Sciences: Applied Mathematics of Transport Theory

这项研究将研究动力学参考理论中出现的初边值问题，特别是Boltzmann，Enskog，B.G.K.的方程和各种修改。寻求解的存在唯一性、正则性和渐近性质。Zweifel和Greenberg教授将继续发展共双半群的扰动理论，特别是在Banach空间背景下，以及相关的Wiener-Hopf分解理论。文中还给出了某些线性化输运方程的显式应用。将数值模拟应用于Vlasov-Poisson系统、木乃伊声学输运和动力学系统的标度性质。这些研究为辐射传输、中子传输和稀薄气体动力学等领域的应用奠定了基础。

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.