Hyperbolic Conservation Laws in Continuum Physics (Grundlehren der mathematischen Wissenschaften)
Edition: 2nd ed. edition
Publisher: Springer
Published: September 29, 2005
Language: eng
Format: Hardcover
Number of pages: 626
ISBN-13: 9783540254522
Subjects: Mathematics; Mechanics - General; Science/Mathematics; Differential Equations; Mechanics - Dynamics - Thermodynamics; Entropy; Mathematics / Differential Equations; Thermodynamics; hyperbolic conservation laws; partial differential equations; Conservation laws (Physics); Differential equations, Hyperbolic; Field theory (Physics)
First sentence: The ambient space for the balance law will be Rk, with typical point X.
Description: This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of the qualitative theory of partial differential equations, whereas the required notions from continuum physics are introduced from scratch. 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. The 2nd edition contains a new chapter recounting the exciting recent developments on the vanishing viscosity method. Numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material, omitted in the first edition, whose relevance and importance has been underscored by current trends in research. In addition, a substantal portion of the original text has been revamped so as to streamline the exposition, enrich the collection of examples and improve the notation. The bibliography has been updated and expanded as well, now comprising over one thousand titles.