具有变重数三特征的hyperbolic operators的Cauchy问题
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
摘要：
研究了一类在$G = Ω\cap \{0 \leq t \leq T\},\: Ω\subset \R^{n+1}$中的三阶双曲型算子$P$在$t = 0$上具有三重特征.本文讨论了当$t = 0$的主象征的基本矩阵有一对非零实特征值且$P$是严格双曲的情形，证明了$P$是强双曲的，即对于任何低阶项$Q$，$P + Q$的Cauchy问题在$G$中是适定的.
英文摘要：
We study a class of third order hyperbolic operators $P$ in $G = Ω\cap \{0 \leq t \leq T\},\: Ω\subset \R^{n+1}$ with triple characteristics on $t = 0$. We consider the case when the fundamental matrix of the principal symbol for $t = 0$ has a couple of non vanishing real eigenvalues and $P$ is strictly hyperbolic for $t > 0.$ We prove that $P$ is strongly hyperbolic, that is the Cauchy problem for $P + Q$ is well posed in $G$ for any lower order terms $Q$.
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