一类半线性弱双曲型方程的初值问题

On the Cauchy problem for a class of semilinear weakly hyperbolic equations

研究如下一类问题其中ｆ∈Ｃ１（Ｒ１），ｆ（０）＝０，ｈ∈Ｈ３（Ｒ２）并具有紧支集，Ｘ１、Ｘ２是Ｒ２上的光滑向量场并满足ｍ阶条件．在以上假设下，得到了问题强解的存在性及正则性．

In this paper,the author studies the problem as follows where with compact support.and are smooth vector-fields in R2 which satisfy the Hormander’s condition of order m.Underthese assumptions,the existence and regularity of the strong solution to the problem is established.