Hyperbolic Conservation Laws and the Compensated Compactness Method
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A01=Yunguang Lu
adiabatic gas flow
advanced hyperbolic systems analysis
applied mathematics
Arbitrary Compact Set
Author_Yunguang Lu
Banach Contraction Mapping Theorem
Bounded Initial Data
Category=PBKJ
Category=PBW
Category=PHU
cauchy
Cauchy Problem
Compact Subset
Compactness Framework
Compensated Compactness Method
Compressible Fluid Flow
Convex Entropy
Dirac Measure
elasticity theory
entropy conditions
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General Euler Equations
Global Weak Solution
Hyperbolic Conservation Laws
hyperbolic differential equations
Hyperbolic System
invariant
Lax Type
Local Smooth Solution
mathematical fluid dynamics
measure
Nonlinear Hyperbolic Systems
nonlinear wave propagation
Ordinary Differential Equations
partial differential equations
problem
riemann
Riemann Invariants
Scalar Conservation Law
solution
Strictly Convex
systems
Unique Smooth Solution
viscosity
Viscosity Solutions
weak
Weak Solution
young
Young Measures
Product details
- ISBN 9780367454739
- Weight: 470g
- Dimensions: 156 x 234mm
- Publication Date: 27 Sep 2002
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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.
Yunguang Lu is a Professor of Mathematics at the University of Columbia, Bogota and at the University of Science and Technology of China, Hefei.
