On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case

DOI10.1007/978-1-4614-6348-1_12zbMath1282.35221OpenAlexW160469962MaRDI QIDQ2848258

Tatsuo Nishitani

Publication date: 26 September 2013

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-6348-1_12

zbMATH Keywords

bicharacteristics\(C^\infty\) well-posednesstransition caseHamiltonian map and flowweighted micro local a priori estimates

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Initial value problems for second-order hyperbolic equations (35L15)

Cites Work

• On the Cauchy problem for noneffectively hyperbolic operators: the Gevrey 4 well-posedness
• On the Cauchy problem for non-effectively hyperbolic operators, the Gevrey 5 well-posedness
• Local energy integrals for effectively hyperbolic operators. I
• The hyperbolic Cauchy problem
• Characterization of pseudodifferential operator and application
• The Cauchy problem for differential equations with double characteristics
• Non effectively hyperbolic operators, Hamilton map and bicharacteristics
• ON THE CAUCHY PROBLEM FOR NON-EFFECTIVELY HYPERBOLIC OPERATORS: THE GEVREY 3 WELL-POSEDNESS
• NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
• The Cauchy Problem for Hyperbolic Operators with Double Characteristics in Presence of Transition
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