Elliptic–Hyperbolic Partial Differential Equations

A Mini-Course in Geometric and Quasilinear Methods

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Elliptic–Hyperbolic Partial Differential Equations by Thomas H. Otway, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Thomas H. Otway ISBN: 9783319197616
Publisher: Springer International Publishing Publication: July 8, 2015
Imprint: Springer Language: English
Author: Thomas H. Otway
ISBN: 9783319197616
Publisher: Springer International Publishing
Publication: July 8, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Treatise on Acoustics by Thomas H. Otway
Cover of the book Currency Cooperation in East Asia by Thomas H. Otway
Cover of the book Squatters and the Politics of Marginality in Uruguay by Thomas H. Otway
Cover of the book Engineering Identities, Epistemologies and Values by Thomas H. Otway
Cover of the book Applications in Electronics Pervading Industry, Environment and Society by Thomas H. Otway
Cover of the book Creative Industries in Europe by Thomas H. Otway
Cover of the book QC-LDPC Code-Based Cryptography by Thomas H. Otway
Cover of the book Artificial Organic Networks by Thomas H. Otway
Cover of the book European Film and Television Co-production by Thomas H. Otway
Cover of the book Fundamentals of Laser-Assisted Micro- and Nanotechnologies by Thomas H. Otway
Cover of the book Industrial Applications of Holonic and Multi-Agent Systems by Thomas H. Otway
Cover of the book Advances in Human Factors and Ergonomics in Healthcare by Thomas H. Otway
Cover of the book Ambient Assisted Living. ICT-based Solutions in Real Life Situations by Thomas H. Otway
Cover of the book Combinatorial Algorithms by Thomas H. Otway
Cover of the book Resource Management for Heterogeneous Wireless Networks by Thomas H. Otway
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy