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The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type (Paperback, 2012)
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The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type (Paperback, 2012)
Series: Lecture Notes in Mathematics, 2043
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Total price: R1,556
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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
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 functions space. Specific
applications to plasma physics, optics, and analysis on projective
spaces are discussed. (From the preface)
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