一类非齐次拟线性双曲型方程组混合初边值问题的整体经典解

The Global Classical Solution of the Mixed Initial-boundary Value Problem for a Kind of the First Order Quasilinear Hyperbolic System

考虑半无界区域{(t,x)|t≥0,x≥0}上的一类拟线性双曲型方程组的混合初边值问题.假设正特征弱线性退化,方程右端项满足匹配条件,可以得到慢衰减小初值问题C1解的整体存在性和唯一性.

The mixed inltial-boundary value problem for a kind of the first order quasilinear hyperbolic system with nonlinear boundary conditions in a half-unbounded domain {（ t ,x） [ t≥0,x≥0} is considerded. Under the assumptions that the positive eigenvalues are weakly linearly degenerate, and that the right hand side of the equations meets matching conditions, the global existence and uniqueness of C^1 solution with small and decaying data are obtained.