EAN: 9783319197609

SPRINGERBRIEFS IN MATHEMATICS ELLIPTIC-HYPERB...

This text is a concise introduction to the partial differential equations which change from
elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming
increasingly important in diverse sub-fields of both applied mathematics and engineering  for
example: - The heating of fusion plasmas by electromagnetic waves- The behaviour of light near
a caustic- Extremal surfaces in the space of special relativity - The formation of rapids 
transonic and multiphase fluid flow - The dynamics of certain models for elastic structures-
The shape of industrial surfaces such as windshields and airfoils - Pathologies of traffic flow
- Harmonic fields in extended projective space They also arise in models for the early universe
for cosmic acceleration  and for possible violation of causality in the interiors of certain
compact stars. Within the past 25 years  they have become central to the isometric embedding of
Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure
mathematics which themselves have important applications. Elliptic-Hyperbolic Partial
Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential
Geometry and Continuum Mechanics held in Edinburgh  Scotland in June 2013. The focus on
geometry in that meeting is reflected in these notes  along with the focus on quasilinear
equations. In the spirit of the ICMS workshop  this course is addressed both to applied
mathematicians and to mathematically-oriented engineers. The emphasis is on very recent
applications and methods  the majority of which have not previously appeared in book form.

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