Some General Properties of a Class of Semilinear Hyperbolic Systems Analogous to the Differential-Integral Equations of Gas Dynamics

摘要

The paper discusses the general structure of a class of semilinear hyperbolic systems analogous to the Boltzmann equations for a gas model with discretized velocity states, using a background of nonequilibrium theory for gas dynamics. The global existence of (nonnegative) solutions associated with nonnegative initial data is developed. Some auxiliary results on a linear conjugacy of systems and on monotonicity and smoothness properties of general (local) solutions are given.