Overview
- Self-contained presentation of the topics
- Starting with a good motivation new ideas are presented in detail, open problems are added
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 159)
Part of the book sub series: Advances in Partial Differential Equations (APDE)
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Table of contents (6 chapters)
Keywords
About this book
It is addressed to beginners as well as specialists in these fields. The contributions are to a large extent self-contained.
Key topics include:
- low regularity solutions to the local Cauchy problem associated with wave maps; local well-posedness, non-uniqueness and ill-posedness results are proved
- coupled systems of wave equations with different speeds of propagation; here pointwise decay estimates for solutions in spaces with hyperbolic weights come in
- damped wave equations in exterior domains; the energy method is combined with the geometry of the exterior domain; for the critical part of the boundary a restricted localized effective dissipation is employed
- the phenomenon of parametric resonance for wave map type equations; the influence of time-dependent oscillations on the existence of global small data solutions is studied - a unified approach to attack degenerate hyperbolic problems as weakly hyperbolic ones and Cauchy problems for strictly hyperbolic equations with non-Lipschitz coefficients
- weakly hyperbolic Cauchy problems with finite time degeneracy; the precise loss of regularity depending on the spatial variables is determined; the main step is to find the correct class of pseudodifferential symbols and to establish a calculus which contains a symmetrizer.
Editors and Affiliations
Bibliographic Information
Book Title: New Trends in the Theory of Hyperbolic Equations
Editors: Michael Reissig, Bert-Wolfgang Schulze
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/3-7643-7386-5
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2005
Hardcover ISBN: 978-3-7643-7283-5Published: 19 July 2005
eBook ISBN: 978-3-7643-7386-3Published: 21 March 2006
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XIII, 514
Topics: Analysis, Partial Differential Equations, Operator Theory, Functional Analysis