Abstract
Using a general existence and uniqueness theory for linear time dependent kinetic equations, for general inhomogeneous multidimensional spatial and velocity domains and partially absorbing boundaries, we obtain local in time solutions of a class of nonlinear Boltzmann type equations. For small initial-boundary data we obtain global in time solutions. The ideal norm on certain ideals in the Banach space ofL p-functions on phase space is used to measure the «size» of initial-boundary data and solutions. Kaniel-Shinbrot type upper and lower approximation arguments are applied. The combined length of the time interval of existence when applying the method repeatedly is analyzed as a function of the size of the initial-boundary data. Specific applications to the nonlinear Boltzmann equation itself and to the plane Broadwell model are given.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call