Hyperbolic Partial Differential Equations
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Hyperbolic Partial Differential Equations
Author: Serge Alinhac
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-06-17
This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
Hyperbolic Partial Differential Equations
Author: Andreas Meister
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The following chapters summarize lectures given in March 2001 during the summerschool on Hyperbolic Partial Differential Equations which took place at the Technical University of Hamburg-Harburg in Germany. This type of meeting is originally funded by the Volkswa genstiftung in Hannover (Germany) with the aim to bring together well-known leading experts from special mathematical, physical and engineering fields of interest with PhD students, members of Scientific Research Institutes as well as people from Industry, in order to learn and discuss modern theoretical and numerical developments. Hyperbolic partial differential equations play an important role in various applications from natural sciences and engineering. Starting from the classical Euler equations in fluid dynamics, several other hyperbolic equations arise in traffic flow problems, acoustics, radiation transfer, crystal growth etc. The main interest is concerned with nonlinear hyperbolic problems and the special structures, which are characteristic for solutions of these equations, like shock and rarefaction waves as well as entropy solutions. As a consequence, even numerical schemes for hyperbolic equations differ significantly from methods for elliptic and parabolic equations: the transport of information runs along the characteristic curves of a hyperbolic equation and consequently the direction of transport is of constitutive importance. This property leads to the construction of upwind schemes and the theory of Riemann solvers. Both concepts are combined with explicit or implicit time stepping techniques whereby the chosen order of accuracy usually depends on the expected dynamic of the underlying solution.
Hyperbolic Partial Differential Equations and Wave Phenomena
Author: Mitsuru Ikawa
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
Deals with initial boundary value problems for second order hyperbolic equations, concentrating on linear hyperbolic equations of second order with a scalar-valued unknown function and elucidating properties of phenomena governed by particular equations. Chapters cover wave phenomena and hyperbolic equations, the existence of a solution for a hyperbolic equation and its properties, construction of asymptotic solutions, and local energy of the wave equation. Includes exercises and solutions. Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo, 1997. Annotation copyrighted by Book News, Inc., Portland, OR