A result on the well posedness of the Cauchy problem for a class of hyperbolic operators with double characteristics
type: Item
instance of: scholarly article
title: A result on the well posedness of the Cauchy problem for a class of hyperbolic operators with double characteristics
zbMATH Open document ID: 0836.47037
author: Milena Petrini
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1996-04-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108362
review text: Summary: Let \(p_2\) be the principal symbol of a hyperbolic differential operator \(P\) of order two admitting characteristic roots of variable multiplicity. Suppose that the double characteristic manifold \(\Sigma\) of \(p_2\) contains a submanifold \(\widetilde {\Sigma}\) such that at each point of \(\widetilde {\Sigma}\) the Hamiltonian matrix of \(p_2\), \(F\), has a Jordan block of dimension 4, whereas at each point of \(\Sigma\setminus \widetilde {\Sigma}\), \(F\) admits only Jordan blocks of size 2 and \(F\) is not effectively hyperbolic. We prove that under suitable conditions on the 3-jet of \(p_2\) at \(\widetilde {\Sigma}\) the Cauchy problem for \(P\) is well posed provided the usual Levi conditions on the lower order terms are satisfied.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 826758
zbMATH Keywords: principal symbol
zbMATH Keywords: hyperbolic differential operator
zbMATH Keywords: characteristic roots
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: Jordan block
zbMATH Keywords: Levi conditions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 826758