非齐次拟线性双曲方程组Goursat问题解的整体存在性

Global classical solutions of Goursat problem for inhomogeneous quasilinear hyperbolic systems

考虑拟线性双曲方程组特征边值问题光滑解的整体存在性.在弱线性退化及匹配条件下,若特征边界上的数据W^(1,1)范数充分小,得到了C^(1)解的整体存在性.为获得解的整体存在性,利用了波相互作用的L^(1)估计,对解建立一致先验估计,进而利用连续延拓的方法确立了解的整体存在性.

This paper considers the global classical solutions of the characteristic boundary value problem for quasilinear hyperbolic systems.When the W^(1,1) norm of characteristic boundary value is sufficiently small,the global existence of C^(1) solution is proved provided that the system is weakly linearly degenerate and satisfies matching condition.In order to obtain the global existence of the solution,the L^(1) estimate of wave interaction is used to establish uniform a priori estimate of the solution,and then the global existence of the solution is established by continuous continuation method.