Hyperbolic Conservation Laws and the Compensated Compactness Method

ISBN-13: 9780367454739 / Angielski / Miękka / 2002 / 256 str.

Yunguang Lu

Opis

The method of compensated compactness as a technique for studying hyperbolic conservation laws holds fundamental importance in many branches of applied mathematics. Until this book appeared, however, most accounts of this method were primarily confined to research papers. Offering the first comprehensive treatment, this monograph makes the material available to a broad audience, gathering together the fundamental ideas and developments into a single work. Beginning with an account of the underlying ideas, it develops applications in a number of key areas, including strictly and nonstrictly hyperbolic systems, elasticity, continuum mechanics, and fluid mechanics.

Recenzje

"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. 2004

Spis treści

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

O autorze

Yunguang Lu is a Professor of Mathematics at the University of Columbia, Bogota and at the University of Science and Technology of China, Hefei.