Hyperbolic conservation laws in continuum physics / Constantine M. Dafermos. (Grundlehren der mathematischen Wissenschaften; 325). ISBN 978-3-662-22021-4. Mathematics Subject Classification (1991): 35L65, 35L67, 73Bxx, 76Lo5. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000. Originally published by Springer-Verlag Berlin Heidelberg New York 2000. Softcover reprint of the hardcover 1st edition 2000. Cover design: MetaDesign plus GmbH, Berlin. Photocomposed from the author's TEX files after editing and reformatting by Kurt Mattes, Heidelberg, using the MathTime fonts and a Springer TEX macro-package. Printed on acid-free paper. SPIN: 10690815 41/3143Ko-5 4 3 2 1 0. For Mihalis and Thalia. The universe is a gigantic system of reflexes produced by shocks. Bernard Shaw ("The black girl in search of God"). Preface: 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 environment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conservation 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 hyperbolic 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,Hyperbolic conservation laws in continuum physics / Constantine M. Dafermos. (Grundlehren der mathematischen Wissenschaften; 325). ISBN 978-3-662-22021-4. Mathematics Subject Classification (1991): 35L65, 35L67, 73Bxx, 76Lo5. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000. Originally published by Springer-Verlag Berlin Heidelberg New York 2000. Softcover reprint of the hardcover 1st edition 2000. Cover design: MetaDesign plus GmbH, Berlin. Photocomposed from the author's TEX files after editing and reformatting by Kurt Mattes, Heidelberg, using the MathTime fonts and a Springer TEX macro-package. Printed on acid-free paper. SPIN: 10690815 41/3143Ko-5 4 3 2 1 0. For Mihalis and Thalia. The universe is a gigantic system of reflexes produced by shocks. Bernard Shaw ("The black girl in search of God"). Preface: 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 environment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conservation 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 hyperbolic 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,