Lecture Notes in Mathematics

The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type

Authors: Otway, Thomas H.

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  • The first text devoted entirely to the analysis of elliptic-hyperbolic equations of Keldysh type
  • Includes the most recent methods of analysis in this field
  • Numerous applications are included
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  • ISBN 978-3-642-24415-5
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About this book

Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)

Reviews

From the book reviews:

“The book is based on Otway’s lectures at Henan University in 2010. These notes are very well written and very useful for readers, particularly advanced researchers and Ph.D. students. Each chapter has its own list of references, its own dynamics, and its own interesting remarks.” (Henryk Leszczyński, Mathematical Reviews, May, 2014)

“The lecture notes were written by the author to supplement a series of ten lectures given at Henan University in the summer of 2010. They are intended for graduate students and researchers in pure or applied analysis with a background in functional analysis -- including Sobolev spaces -- and the basic theory of partial differential equations. The book contains 6 chapters (every one with its references), summary, addenda, directions for future research and index.” (Elena Gavrilova, Zentralblatt MATH, Vol. 1246, 2012)

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Introduction

    Pages 1-11

    Otway, Thomas H.

  • Mathematical Preliminaries

    Pages 13-45

    Otway, Thomas H.

  • The Equation of Cinquini-Cibrario

    Pages 47-85

    Otway, Thomas H.

  • The Cold Plasma Model

    Pages 87-120

    Otway, Thomas H.

  • Light Near a Caustic

    Pages 121-144

    Otway, Thomas H.

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-24415-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2043
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-24415-5
DOI
10.1007/978-3-642-24415-5
Softcover ISBN
978-3-642-24414-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 214
Number of Illustrations
15 b/w illustrations, 11 illustrations in colour
Topics