Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics) free ebook download.

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Cauchy Problem for Differential Operators with Double Characteristics: Non-Effectively Hyperbolic Characteristics (Lecture Notes in Mathematics) free ebook download

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Author(s):	Tatsuo Nishitani

Date:	2017-12-23	Format:	PDF,EPUB	Language:	English	ISBN/ASIN:	3319676113
Pages:	213	OCR:		Quality:		ISBN13:	9783319676111
Uploader:	stirkout	Upload Date:	11/26/2017 12:29:26 AM

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Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for dierential operators with non-eectively hyperbolic double characteristics. Previously scattered over numerous dierent 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 dierential operator P of order m (i.e. one where Pm = dPm = 0) is eectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is eectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.
If there is a non-eectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between Pj and Pj , where ij are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4  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.
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Tags: Cauchy Characteristics Differential Double Hyperbolic Lecture Mathematics Notes Operators Problem

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