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Titlebook: Elliptic–Hyperbolic Partial Differential Equations; A Mini-Course in Geo Thomas H. Otway Book 2015 The Author(s) 2015 Boundary Value Proble

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书目名称Elliptic–Hyperbolic Partial Differential Equations
副标题A Mini-Course in Geo
编辑Thomas H. Otway
视频video
概述Studies concrete examples in detail, to illustrate a wide variety of methods.Begins from basic material, introducing mixed-type problems in different applications.Provides a grand view of mixed-type e
丛书名称SpringerBriefs in Mathematics
图书封面Titlebook: Elliptic–Hyperbolic Partial Differential Equations; A Mini-Course in Geo Thomas H. Otway Book 2015 The Author(s) 2015 Boundary Value Proble
描述.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 IC
出版日期Book 2015
关键词Boundary Value Problem; Busemann Equation; Bäcklund Transformation; Elliptic—Hyperbolic Systems; Free Bo
版次1
doihttps://doi.org/10.1007/978-3-319-19761-6
isbn_softcover978-3-319-19760-9
isbn_ebook978-3-319-19761-6Series ISSN 2191-8198 Series E-ISSN 2191-8201
issn_series 2191-8198
copyrightThe Author(s) 2015
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Hodograph and Partial Hodograph Methods,tations into the study of an elliptic–hyperbolic equation. The . hodograph transformation dates from the 1930s, but its application to elliptic–hyperbolic equations is relatively recent; our treatment follows the work of S.-X. Chen. In addition, various methods are given for constructing explicit so
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Boundary Value Problems,sonic lines having curvature. Recent work of S.-X. Chen on the nonlinear Lavrent’ev–Bitsadze equation is emphasized. A mixed Dirichlet–Neumann problem for an equation that arises in the context of plasma heating is reviewed; that problem introduces a tiny part of the deep theory on weak solutions to
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,Bäcklund Transformations and Hodge-Theoretic Methods,ussed in detail. Topics include a systematic method for producing Bäcklund transformations via the Hodge duality operator. The method is useful for the frequent cases in which the model equations can be expressed as nonlinear Hodge–Frobenius equations. A hierarchy of constraints for geometric variat
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Agency and Scene in Jane Austen, of explicit solutions to a large and useful class of quasilinear elliptic–hyperbolic systems on both sides of the sonic transition. An example shows how the individual solutions on the elliptic and hyperbolic regions can be pasted together to produce a solution which crosses the sonic line with continuity.
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Hodograph and Partial Hodograph Methods, of explicit solutions to a large and useful class of quasilinear elliptic–hyperbolic systems on both sides of the sonic transition. An example shows how the individual solutions on the elliptic and hyperbolic regions can be pasted together to produce a solution which crosses the sonic line with continuity.
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