Hyperbolic Conservation Laws and the Compensated Compactness Method

Hyperbolic Conservation Laws and the Compensated Compactness Method

By (author)  , By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 11 business days
When will my order arrive?

Description

The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments. The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity solutions, and introduce the Invariant Region Theory. The study then turns to methods for symmetric systems of two equations and two equations with quadratic flux, and the extension of these methods to the Le Roux system. After examining the system of polytropic gas dynamics (g-law), the authors first study two special systems of one-dimensional Euler equations, then consider the general Euler equations for one-dimensional compressible fluid flow, and extend that method to systems of elasticity in L8 space. Weak solutions for the elasticity system are introduced and an application to adiabatic gas flow through porous media is considered. The final four chapters explore applications of the compensated compactness method to the relaxation problem. With its careful account of the underlying ideas, development of applications in key areas, an inclusion of the author's own contributions to the field, this monograph will prove a welcome addition to the literature and to your library.show more

Product details

  • Hardback | 256 pages
  • 166.1 x 243.8 x 18.8mm | 517.1g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 10 black & white illustrations
  • 1584882387
  • 9781584882381

Review quote

"The book is carefully written and will be appreciated both by PhD students and experts in the field as one of a few books gathering the knowledge [previously] dispersed among research papers." - EMS Newsletter, Dec. 2004show more

Table of contents

PRELIMINARY THEORY OF COMPENSATED COMPACTNESS SCALAR EQUATION ELEMENTARY IN HYPERBOLIC SYSTEM A SYMMETRY SYSTEM A SYSTEM OF QUADRATIC FLUX LE ROUX SYSTEM SYSTEM OF POLYTROPIC GAS DYNAMICS TWO SYSTEMS OF EULER-EQUATIONS GENERAL SYSTEM OF EULER-EQUATIONS EXTENDED SYSTEMS OF ELASTICITY L[p] CASE FOR SYSTEMS OF ELASTICITY ELEMENTARY IN RELAXATION RELAXATION WITH DIFFUSION SYSTEMS WITH STIFF RELAXATION RELAXATION FOR 3 x 3 SYSTEMS BIBLIOGRAPHYshow more