Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves

Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves

by Denis Serre
     
 

ISBN-10: 0521582334

ISBN-13: 9780521582339

Pub. Date: 01/28/2011

Publisher: Cambridge University Press

Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws describing the physical models and…  See more details below

Overview

Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self contained, with large numbers of exercises and full discussion of all the ideas. This makes it an ideal text for graduate courses in the area of partial differential equations.

Read More

Product Details

ISBN-13:
9780521582339
Publisher:
Cambridge University Press
Publication date:
01/28/2011
Pages:
286
Product dimensions:
6.85(w) x 9.72(h) x 0.67(d)

Table of Contents

1. Some models; 2. Scalar equations in dimension d = 1; 3. Linear and quasi-linear systems; 4. Dimension d = 1, the Riemann problem; 5. Glimm's method; 6. Second order perturbations; 7. Viscosity profiles of shock waves; Bibliography; Index.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >