Advances in Partial Differential Equations

New Trends in the Theory of Hyperbolic Equations

Editors: Reissig, Michael, Schulze, Bert-Wolfgang (Eds.)

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About this book

The present volume is dedicated to modern topics of the theory of hyperbolic equations such as evolution equations, multiple characteristics, propagation phenomena, global existence, influence of nonlinearities.
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.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Wave Maps and Ill-posedness of their Cauchy Problem

    Pages 1-111

    D’Ancona, Piero (et al.)

  • On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations

    Pages 113-211

    Kubo, Hideo (et al.)

  • Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains

    Pages 213-299

    Nakao, Mitsuhiro

  • Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation

    Pages 301-385

    Yagdjian, Karen

  • On the Nonlinear Cauchy Problem

    Pages 387-448

    Cicognani, Massimo (et al.)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-7643-7386-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
New Trends in the Theory of Hyperbolic Equations
Editors
  • Michael Reissig
  • Bert-Wolfgang Schulze
Series Title
Advances in Partial Differential Equations
Series Volume
159
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7386-3
DOI
10.1007/3-7643-7386-5
Hardcover ISBN
978-3-7643-7283-5
Series ISSN
2504-3587
Edition Number
1
Number of Pages
XIII, 514
Topics