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 andto 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. 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 collectionof applications has been substantially enriched. The bibliography, also expanded and updated, now comprises over fifteen hundred titles. The author is unquestionably the greatest authority on the subject as well as a masterly writer The 3rd edition is thoroughly revised, up-to-date and includes new material onthe early history of the subject, and a new chapter recounting recent solution of open problems of long standing in classical aerodynamics The expanded bibliography comprises now over fifteen hundred titles INDICE: Preface.- Acknowledgments.- Introduction.- A Sketch of the Early History of Hyperbolic Conservation Laws.- I.Balance Laws.- II.Introduction to Continuum Physics.- III.Hyperbolic Systems of Balance Laws.- IV.The Cauchy Problem.- V.Entropy and the Stability of Classical Solutions.- VI.The L1 Theory for Scalar Conservation Laws.- VII.Hyperbolic Systems of Balance Laws in One-Space Dimension.- VIII.Admissible Shocks.- IX.AdmissibleWave Fans and the RiemannProblem.- X.Generalized Characteristics.- XI.Genuinely Nonlinear Scalar Conservation Laws.- XII.Genuinely Nonlinear Systems of Two Conservation Laws.- XIII.The Random Choice Method.- XIV.The Front Tracking Method and Standard RiemannSemigroups.- XV.Construction of BV Solutions by the Vanishing Viscosity Method.- XVI.Compensated Compactness.-XVII.Conservation Laws in Two Space Dimensions.- Bibliography.- Author Index.- Subject Index.
- ISBN: 978-3-642-04047-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 720
- Fecha Publicación: 19/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés