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

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 su...

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Main Author: LeFloch, Philippe G.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel Birkhäuser Basel 2002, 2002
Edition:1st ed. 2002
Series:Lectures in Mathematics. ETH Zürich
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Hyperbolic Systems of Conservation Laws  |h Elektronische Ressource  |b The Theory of Classical and Nonclassical Shock Waves  |c by Philippe G. LeFloch 
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505 0 |a I. Fundamental concepts and examples -- 1. Hyperbolicity, genuine nonlinearity, and entropies -- 2. Shock formation and weak solutions -- 3. Singular limits and the entropy inequality -- 4. Examples of diffusive-dispersive models -- 5. Kinetic relations and traveling waves -- 1. Scalar Conservation Laws -- II. The Riemann problem -- III. Diffusive-dispersive traveling waves -- IV. Existence theory for the Cauchy problem -- V. Continuous dependence of solutions -- 2. Systems of Conservation Laws -- VI. The Riemann problem -- VII. Classical entropy solutions of the Cauchy problem -- VIII. Nonclassical entropy solutions of the Cauchy problem -- IX. Continuous dependence of solutions -- X. Uniqueness of entropy solutions 
653 |a Mathematical analysis 
653 |a Partial Differential Equations 
653 |a Analysis (Mathematics) 
653 |a Partial differential equations 
653 |a Analysis 
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520 |a 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