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Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Elliptic–Hyperbolic Partial Differential Equations/ by Thomas H. Otway.
其他題名:	A Mini-Course in Geometric and Quasilinear Methods /
作者:	Otway, Thomas H.
面頁冊數:	VII, 128 p. 15 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial differential equations. -
電子資源:	https://doi.org/10.1007/978-3-319-19761-6
ISBN:	9783319197616

Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /
Otway, Thomas H.

Elliptic–Hyperbolic Partial Differential EquationsA Mini-Course in Geometric and Quasilinear Methods /[electronic resource] :by Thomas H. Otway. - 1st ed. 2015. - VII, 128 p. 15 illus., 6 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Introduction -- Overview of elliptic–hyperbolic PDE -- Hodograph and partial hodograph methods -- Boundary value problems -- B¨acklund transformations and Hodge-theoretic methods -- Natural focusing.

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.

ISBN: 9783319197616

Standard No.: 10.1007/978-3-319-19761-6doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /
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