高维半线性二阶双曲型方程分片光滑解的反射

REFLECTION OF PIECEWISE SMOOTH SOLUTION TO SECOND ORDER HYPERBOLIC BQUATIONS IN HIGHER DIMENSION

讨论半线性二阶双曲型方程的边值问题，设∑￣－是下半空间中的特征面，∑￣＋是∑￣－在上半空间中的反射特征面，我们得到了下面的结果：若解在下半空间关于∑￣－是分片光滑的，则它上半空间关于∑￣＋是分片光滑的。

In this paper,We discuss the boundary problems of semilinear hyperbolic eqations inhigher dimersions.Suppose that ∑￣- is a characteristic surface in the psat,∑￣+is the reflectedcharacteristic surface of ∑￣-the following result is obtained.If solution is piecewise smooth withrespect to ∑￣-in the past then the solution is piecewise smooth with respect to ∑￣+ in the fu-ture.