二阶弱双曲方程的混合边值问题

ON THE MIXED BOUNDARY VALUE PROBLEMS FOR WEAKLY HYPERBOLIC EQUATIONS OF SECOND ORDER

在柱形区域Q_T=Ω×[0,T]内考虑下述弱双曲方程的混合边值问题其中Ω是R^n中具有光滑边界的紧流形,系数光滑且属于(?)(Q_T),且本文有下述定理:若条件(1.4)-(1.7)满足,且α_(ij),α_1,α_o,α,b_j∈(?)(Q_T),α_(ij)(x,t)ξ_iξ_j≥则问题(1.1)～(1.3)存在唯一解u∈H^(∞)(Q_T),文[5]的结果是定理当α≡1,α_(ij)=t^k(?),(?)ξ_iξ_j≥d|ξ|~2的特殊情况.

We consider the following problem in a cylindrical domainwhere Q is a compact variety with smooth boundary, all the coefficients and f belong to , especially is the symmetric nonnegative matrix, a, b are nonnegative smooth functions, bat their are not equal to zero simultaneously. In the paper we have the following results Theorem Assume that conditionsLet . Then there exists a unique solution of the problem ( I ), which provided that the data satisty the compatibilty condition of infinite order. In [5] Kubo's result is the special case of this Theorem.