Abstract
We discuss the well-posedness of the Cauchy problem for noneffectively hyperbolic operators assuming that the spectral structure of the Hamilton map changes across a submanifold of codimension 1 of the double characteristic manifold. Under the assumption that there is no null bicharacteristic tangent to the submanifold where the spectral transition occurs, we derive microlocal a priori estimates assuming the strict Ivrii-Petkov-Hörmander condition.
2010 Mathematics Subject Classification: Primary: 35L15; Secondary: 35B30.
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Nishitani, T. (2013). On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case. In: Cicognani, M., Colombini, F., Del Santo, D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol 84. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6348-1_12
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DOI: https://doi.org/10.1007/978-1-4614-6348-1_12
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