Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves

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Springer Science & Business Media, Jul 1, 2002 - Mathematics - 294 pages
This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would like to thank the faculty of the Mathematics Department, and especially Rolf Jeltsch and Michael Struwe, for giving me such a great opportunity to deliver the lectures in a very stimulating environment. Part of this material was also taught earlier as an advanced graduate course at the Ecole Poly technique (Palaiseau) during the years 1995-99, at the Instituto Superior Tecnico (Lisbon) in the Spring 1998, and at the University of Wisconsin (Madison) in the Fall 1998. This project started in the Summer 1995 when I gave a series of lectures at the Tata Institute of Fundamental Research (Bangalore). One main objective in this course is to provide a self-contained presentation of the well-posedness theory for nonlinear hyperbolic systems of first-order partial differential equations in divergence form, also called hyperbolic systems of con servation laws. Such equations arise in many areas of continuum physics when fundamental balance laws are formulated (for the mass, momentum, total energy . . . of a fluid or solid material) and small-scale mechanisms can be neglected (which are induced by viscosity, capillarity, heat conduction, Hall effect . . . ). Solutions to hyper bolic conservation laws exhibit singularities (shock waves), which appear in finite time even from smooth initial data.
 

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Contents

Treatment of Anaphoric Problems in Referentially Opaque Contexts
1
Knowledge Processing in the LILOG Project From the First to the Second
26
Indexicality and Representation
50
Steps towards Intelligent Text Processing
70
Ch Habel 94
116
On the Logical Structure of Comparatives
146
Aspects of Consistency of Sophisticated Knowledge Representation Languages
168
Unification Based Machine Translation
191
Diffusivedispersive traveling waves
51
Existence theory for the Cauchy problem
81
Continuous dependence of solutions
118
The Riemann problem
139
Classical entropy solutions of the Cauchy problem
167
Nonclassical entropy solutions of the Cauchy problem
188
Continuous dependence of solutions
212
Uniqueness of entropy solutions
241

Perspectives in MultipleValued Logic
206
Properties and Actions
221
Preface ix
The Riemann problem
29
Appendix Functions with bounded variation
259
Bibliographical notes
265
References
271
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