非齐次线性退化双曲方程组的整体经典解

Global Classical Solutions for Inhomogeneous Linearly Degenerate Hyperbolic Systems

主要考虑非齐次线性退化双曲方程组具有周期初值的经典解的整体存在性.我们知道,对于齐次精形,周期的初值即使很小,整体经典解一般不会存在.因此,本文重点讨论非齐次项对经典解存在性的影响,特别是阻尼项和粘性项的影响.

In this paper we consider the global existence of classical solutions to the Cauchy problem for inhomogeneous linearly degenerate hyperbolic systems with periodic initial data .It is well known that for the homogeneous case ,the classical solutions generally can not exist for all time no matter how small the norm of periodic initial data are .Thus ,in this paper our focus is to investigate the impact of source terms on the global existence of classical solutions .The source terms considered here include the damping terms and viscosity terms .