Cauchy Problem for Differential Operators with Double Characteristics [e-book]: Non-Effectively Hyperbolic Characteristics / Tatsuo Nishitani

• Autore: Nishitani, Tatsuo
• Descrizione fisica: 1 online resource (viii, 211 pages) : illustrations
• Disciplina: 515.353
• Soggetto topico: Differential equations, Partial; Ordinary Differential Equations
• Classificazione: AMS 35-02; LC QA370-380
• Nota di bibliografia: Includes bibliographical references and index
• Nota di contenuto: 1. Introduction ; 2 Non-effectively hyperbolic characteristics.- 3 Geometry of bicharacteristics.- 4 Microlocal energy estimates and well-posedness.- 5 Cauchy problemno tangent bicharacteristics. - 6 Tangent bicharacteristics and ill-posedness.- 7 Cauchy problem in the Gevrey classes.- 8 Ill-posed Cauchy problem, revisited ; References
• Sommario/riassunto: Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for di erential operators with non-e ectively hyperbolic double characteristics. Previously scattered over numerous di erent publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a di erential operator P of order m (i.e. one where Pm = dPm = 0) is e ectively hyperbolic if the Hamilton map FPm has real non-zero eigenvalues. When the characteristics are at most double and every double characteristic is e ectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-e ectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between Pæj and P æj , where iæj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 ₉ 4 Jordan block, the spectral structure of FPm is insucient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role
• ISBN: 9783319676128; 3319676121; 9783319676111; 3319676113
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 991003576719707536
• Lo trovi qui: Univ. del Salento
• Localizzazioni e accesso elettronico: https://link.springer.com/book/10.1007/978-3-319-67612-8#toc
• Serie: Lecture Notes in Mathematics, 0075-8434 ; 2202