Non-linear hyperbolic equations in domains with conical points : existence and regularity of solutions
Author(s)
Bibliographic Information
Non-linear hyperbolic equations in domains with conical points : existence and regularity of solutions
(Mathematical research = Mathematische Forschung, Bd. 84)
Akademie Verlag , VCH, c1995
1st ed
Available at 10 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
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  United States of America
Note
Includes bibliographical references
Description and Table of Contents
Description
In the first part of these notes, the existence of solutions to the corresponding linear equations is addressed, including the asymptotics of solutions near conical points. Using this information, the quasilinear equations are then solved by the standard iteration procedure. The exposition is based upon Kato's semigroup-theoretic approach for solving abstract linear hyperbolic equations and Schulze's theory of pseudo-differential operators on manifolds with conical singularities. The former method provides the general framework, whereas the latter is the basic tool in treating the specific difficulties of the non-smooth situation. Significantly, Schulze's theory admits a parameter-dependent version, which allows the description of the branching behaviour in time of discrete asymptotics of solutions near conical points. The calculus is presented in a form in which the operators are permitted to have symbols with limited smoothness, as arises in nonlinear problems. In an appendix, the applicability of energy methods is briefly discussed.
Table of Contents
- Hyperbolic partial differential equations
- pseudo-differential operators
- operators with non-smooth symbols
- operators on manifolds with conical singularities
- Kato's semigroup-theoretic approach for solving linear hyperbolic equations
- energy estimates
- branching behaviour of discrete asymptotics of solutions near conical points. (Part contents).
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