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Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics
Catalogue Information
Field name Details
Dewey Class 515.353
Title Hyperbolic Conservation Laws in Continuum Physics ([EBook]) / by Constantine M. Dafermos.
Author Dafermos, Constantine M. , 1941-
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 2000.
Physical Details XVI, 446 pages, 5 illus. : online resource.
Series Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 325
ISBN 9783662220191
Summary Note The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi­ ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva­ tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper­ bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.:
Contents note I. Balance Laws -- II. Introduction to Continuum Physics -- III. Hyperbolic Systems of Balance Laws -- IV. The Initial-Value Problem: Admissibility of Solutions -- V. Entropy and the Stability of Classical Solutions -- VI. The L1 Theory of the Scalar Conservation Law -- VII. Hyperbolic Systems of Balance Laws in One-Space Dimension -- VIII. Admissible Shocks -- IX. Admissible Wave Fans and the Riemann Problem -- 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 Riemann Semigroups -- XV. Compensated Compactness -- Author Index.
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