The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type

  • Thomas H.¬†Otway

Part of the Lecture Notes in Mathematics book series (LNM, volume 2043)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Thomas H. Otway
    Pages 1-11
  3. Thomas H. Otway
    Pages 13-45
  4. Thomas H. Otway
    Pages 47-85
  5. Thomas H. Otway
    Pages 87-120
  6. Thomas H. Otway
    Pages 121-144
  7. Thomas H. Otway
    Pages 145-167
  8. Back Matter
    Pages 169-214

About this book

Introduction

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 that can be formulated for Keldysh-type equations, 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 placed on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space, and specific applications to plasma physics, optics, and analysis on projective spaces are discussed.

Keywords

35-XX, 35M10 boundary value problems elliptic-hyperbolic equations equations of Keldysh type

Authors and affiliations

  • Thomas H.¬†Otway
    • 1
  1. 1.Department of Mathematical SciencesYeshiva UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-24415-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-24414-8
  • Online ISBN 978-3-642-24415-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book