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

Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves
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Field name Details
Dewey Class 515
Title Hyperbolic Systems of Conservation Laws ([EBook] :) : The Theory of Classical and Nonclassical Shock Waves / by Philippe G. LeFloch.
Author LeFloch, Philippe G.
Other name(s) SpringerLink (Online service)
Publication Basel : Birkhäuser , 2002.
Physical Details X, 294 pages : online resource.
Series Lectures in mathematics / ETH Zürich
ISBN 9783034881500
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-0348-8150-0
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