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arXiv · 1010.3113

Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Enrico Bernardi·Antonio Bove·Vesselin Petkov
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Abstract

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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Enrico Bernardi, Antonio Bove, Vesselin Petkov. 2010-10-15. Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity. https://arxiv.org/abs/1010.3113

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