The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type (Lecture Notes in Mathematics, Band 2043) - Softcover

Otway, Thomas H. H.

Softcover

ISBN 10: 3642244149 ISBN 13: 9783642244148

Verlag: Springer, 2012

Inhaltsangabe

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)

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Über die Autorin bzw. den Autor

The author's research includes contributions to the mathematical theory of plasma heating in tokamaks, elliptic-hyperbolic extensions of nonlinear Hodge theory and partial differential equations in extended projective space. He is the author of the text, The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type (2012), published by Springer Berlin Heidelberg.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 3642244149
• ISBN 13: 9783642244148
• Einband: Taschenbuch
• Anzahl der Seiten: 228
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