Elliptic–Hyperbolic Partial Differential Equations: A Mini-Course in Geometric and Quasilinear Methods: SpringerBriefs in Mathematics
Autor Thomas H. Otwayen Limba Engleză Paperback – 21 iul 2015
• 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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Specificații
ISBN-13: 9783319197609
ISBN-10: 3319197606
Pagini: 130
Ilustrații: VII, 128 p. 15 illus., 6 illus. in color.
Dimensiuni: 155 x 235 x 9 mm
Greutate: 0.2 kg
Ediția:1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3319197606
Pagini: 130
Ilustrații: VII, 128 p. 15 illus., 6 illus. in color.
Dimensiuni: 155 x 235 x 9 mm
Greutate: 0.2 kg
Ediția:1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Mathematics
Locul publicării:Cham, Switzerland
Public țintă
GraduateCuprins
Introduction.- Overview of elliptic–hyperbolic PDE.- Hodograph and partial hodograph methods.- Boundary value problems.- B¨acklund transformations and Hodge-theoretic methods.- Natural focusing.
Notă biografică
The 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.
Caracteristici
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 equations, from basic materials to recent progress and emerging applications Includes supplementary material: sn.pub/extras