TY  - BOOK
AU  - Dafermos,Constantine M.
ED  - SpringerLink (Online service)
TI  - Hyperbolic Conservation Laws in Continuum Physics
T2  - Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
SN  - 9783642040481
AV  - QA370-380 
U1  - 515.353 23
PY  - 2010///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differential equations, partial
KW  - Mechanics
KW  - Thermodynamics
KW  - Materials
KW  - Mechanical engineering
KW  - Partial Differential Equations
KW  - Continuum Mechanics and Mechanics of Materials
KW  - Structural Mechanics
N1  - Balance Laws -- to Continuum Physics -- Hyperbolic Systems of Balance Laws -- The Cauchy Problem -- Entropy and the Stability of Classical Solutions -- The Theory for Scalar Conservation Laws -- Hyperbolic Systems of Balance Laws in One-Space Dimension -- Admissible Shocks -- Admissible Wave Fans and the Riemann Problem -- Generalized Characteristics -- Genuinely Nonlinear Scalar Conservation Laws -- Genuinely Nonlinear Systems of Two Conservation Laws -- The Random Choice Method -- The Front Tracking Method and Standard Riemann Semigroups -- Construction of Solutions by the Vanishing Viscosity Method -- Compensated Compactness -- Conservation Laws in Two Space Dimensions
N2  - This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. New to the 3rd edition is an account of the early history of the subject, spanning the period between 1800 to 1957. Also new is a chapter recounting the recent solution of open problems of long standing in classical aerodynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised and brought up to date, and the collection of applications has been substantially enriched. The bibliography, also expanded and updated, now comprises over fifteen hundred titles. From the reviews of the 2nd edition: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful." Katarina Jegdic, SIAM Review
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-04048-1
ER  -