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OverviewThis 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. Full Product DetailsAuthor: Thomas H. OtwayPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2015 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 2.488kg ISBN: 9783319197609ISBN 10: 3319197606 Pages: 128 Publication Date: 21 July 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsIntroduction.- Overview of elliptic–hyperbolic PDE.- Hodograph and partial hodograph methods.- Boundary value problems.- B¨acklund transformations and Hodge-theoretic methods.- Natural focusing.ReviewsAuthor InformationThe 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. Tab Content 6Author Website:Countries AvailableAll regions |
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