Elliptic–Hyperbolic Partial Differential Equations Elliptic–Hyperbolic Partial Differential Equations
SpringerBriefs in Mathematics

Elliptic–Hyperbolic Partial Differential Equations

A Mini-Course in Geometric and Quasilinear Methods

    • $39.99
    • $39.99

Publisher Description

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.

GENRE
Science & Nature
RELEASED
2015
July 8
LANGUAGE
EN
English
LENGTH
135
Pages
PUBLISHER
Springer International Publishing
SELLER
Springer Nature B.V.
SIZE
2.7
MB

More Books Like This

Handbook of Differential Equations: Evolutionary Equations Handbook of Differential Equations: Evolutionary Equations
2008
Modern Problems in Applied Analysis Modern Problems in Applied Analysis
2018
Analysis and Numerics of Partial Differential Equations Analysis and Numerics of Partial Differential Equations
2012
Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions
2017
Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering
2019
Fundamental Solutions of Linear Partial Differential Operators Fundamental Solutions of Linear Partial Differential Operators
2015

Other Books in This Series

Twisted Isospectrality, Homological Wideness, and Isometry Twisted Isospectrality, Homological Wideness, and Isometry
2023
Brakke's Mean Curvature Flow Brakke's Mean Curvature Flow
2019
Geodesic Convexity in Graphs Geodesic Convexity in Graphs
2013
Continuous Average Control of Piecewise Deterministic Markov Processes Continuous Average Control of Piecewise Deterministic Markov Processes
2013
Spectra and Normal Forms Spectra and Normal Forms
2024
Deep Learning for Fluid Simulation and Animation Deep Learning for Fluid Simulation and Animation
2023