Abstract
We prove that the Cauchy problem for a class of hyperbolic operators with double characteristics and whose simple null bicharacteristics have limit points on the set of double points is not well posed in the C ∞ category, even though the usual Ivrii-Petkov conditions on the lower order terms are satisfied.
According to the standard linear algebra classification these operators, at a double point, have fundamental matrices exhibiting a Jordan block of size 4 and cannot be brought into a canonical form known as “Ivrii decomposition”, due to higher order non-vanishing terms in the Taylor development of the principal symbol near the given double point.
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Bernardi, E., Bove, A. (2006). On the Cauchy problem for some hyperbolic operator with double characteristics. In: Bove, A., Colombini, F., Del Santo, D. (eds) Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 69. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4521-2_3
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DOI: https://doi.org/10.1007/978-0-8176-4521-2_3
Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-4521-2
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