Lu Hyperbolic Conservation Laws and the Compensated Compactness Method

Erscheinungsjahr 2010
ISBN: 978-1-4200-3557-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 256 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

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.

Zielgruppe

Applied mathematicians, and engineers in partial differential equations, engineering mathematics, elasticity, fluid mechanics, and mechanics of solids

Autoren/Hrsg.

Lu, Yunguang

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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
BIBLIOGRAPHY