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140122  eng 
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a 9783034881500

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a LeFloch, Philippe G.

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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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a 1st ed. 2002

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a Basel
b Birkhäuser Basel
c 2002, 2002

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a X, 294 p
b online resource

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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 diffusivedispersive models  5. Kinetic relations and traveling waves  1. Scalar Conservation Laws  II. The Riemann problem  III. Diffusivedispersive 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

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a Mathematical analysis

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a Partial Differential Equations

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a Analysis (Mathematics)

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a Partial differential equations

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a Analysis

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a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Lectures in Mathematics. ETH Zürich

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u https://doi.org/10.1007/9783034881500?nosfx=y
x Verlag
3 Volltext

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a 515

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a This set of lecture notes was written for a NachdiplomVorlesungen 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 199599, 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 selfcontained presentation of the wellposedness theory for nonlinear hyperbolic systems of firstorder 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 smallscale 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
