Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Details Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

2010-10-15

arxiv.org/abs/1010.3113v1

Mathematics

Analysis of PDEs

Scientific paper

We study a class of third order hyperbolic operators $P$ in $G = \Omega \cap \{0 \leq t \leq T\},\: \Omega \subset \R^{n+1}$ 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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