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中文摘要：
考虑一阶拟线性双曲型方程组的柯西问题.假设特征弱线性退化,非齐次项满足相应与此特征的匹配条件,初值满足慢衰减小,得到拟线性严格双曲型方程组柯西问题的整体经典解的存在性.在整体经典解存在的基础上,采用正规化坐标和波的分解公式得到拟线性双曲型方程组解的一些模的先验估计,证明了解的逐点衰减估计.
英文摘要：
The Cauchy problem of first order quasilinear hyperbolic equations was considerded.Under the assum-ptions that the eigenvalues are weakly linearly degenerste,the non-homogeneous items meet the corresponding with the characteristics of the matching conditions,and Initial value satisfies slow attenuation is small,the global existence of quasilinear hyperbolic differential equations of Cauchy problem was obtained.On the basis of global classical solution exists,using normalized coordinates and wave decomposition theorem,some prior estimates of the molds of quasilinear hyperbolic equations was obtained,point by point decay estimate was proved.
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