The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type / by Thomas H. Otway.

Format:

Book

Author/Creator:

Otway, Thomas H., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2043.

Lecture Notes in Mathematics, 0075-8434 ; 2043

Language:

English

Subjects (All):

Differential equations, Partial.

Partial Differential Equations.

Local Subjects:

Partial Differential Equations.

Physical Description:

1 online resource (IX, 214 pages 26 illustrations, 11 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.

System Details:

text file PDF

Summary:

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.

Contents:

1 Introduction

2 Mathematical Preliminaries

3 The Equation of Cinquini-Cibrario

4 The Cold Plasma Model

5 Light near a Caustic

6 Projective Geometry.

Other Format:

Printed edition:

ISBN:

9783642244155

Access Restriction:

Restricted for use by site license.