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Microlocal Analysis and Nonlinear Waves

Author: Michael Beals; Richard B Melrose; Jeffrey Rauch
Publisher: New York, NY : Springer New York, 1991.
Series: IMA volumes in mathematics and its applications, 30.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The behavior of linear hyperbolic waves has been analyzed by decomposing the waves into pieces in space-time and into different frequencies. The linear nature of the equations involved allows the reassembling of the pieces in a simple fashion; the individual pieces do not interact. For nonlinear waves the interaction of the pieces seemed to preclude such an analysis, but in the late 1970s it was shown that a similar  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Beals; Richard B Melrose; Jeffrey Rauch
ISBN: 9781461391364 1461391369
OCLC Number: 852789067
Description: 1 online resource (xiii, 199 pages 18 illustrations).
Contents: On the interaction of conormal waves for semilinear wave equations --
Regularity of nonlinear waves associated with a cusp --
Evolution of a punctual singularity in an Eulerian flow --
Water waves, Hamiltonian systems and Cauchy integrals --
Infinite gain of regularity for dispersive evolution equations --
On the fully non-linear Cauchy problem with small data. II --
Interacting weakly nonlinear hyperbolic and dispersive waves --
Nonlinear resonance can create dense oscillations --
Lower bounds of the life-span of small classical solutions for nonlinear wave equations --
Propagation of stronger singularities of solutions to semilinear wave equations --
Conormality, cusps and non-linear interaction --
Quasimodes for the Laplace operator and glancing hypersurfaces --
A decay estimate for the three-dimensional inhomogeneous Klein-Gordon equation and global existence for nonlinear equations --
Interaction of singularities and propagation into shadow regions in semilinear boundary problems.
Series Title: IMA volumes in mathematics and its applications, 30.
Responsibility: edited by Michael Beals, Richard B. Melrose, Jeffrey Rauch.

Abstract:

If P( t, x, Dt,x) is a strictly hyperbolic operator or system then the singular support of f gives an upper bound for the singular support of u (Courant-Lax, Lax, Ludwig), namely singsupp u C the  Read more...

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