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Elliptic-Hyperbolic Partial Differential Equations - A Mini-Course in Geometric and Quasilinear Methods (Paperback, 1st ed. 2015)
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Elliptic-Hyperbolic Partial Differential Equations - A Mini-Course in Geometric and Quasilinear Methods (Paperback, 1st ed. 2015)
Series: SpringerBriefs in Mathematics
Expected to ship within 10 - 15 working days
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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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