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Denis Serre Systems of Conservation Laws 1_ Hyperbolicity, Entropies, Shock Waves 1999.pdf

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Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves CAMBRIDGE UNIVERSITY PRESS DENIS SERRE Translated by I . N. SNEDDON Systems of Conservation Laws 1 Systems of conservation laws arise naturally in several areas of physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conse
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  Systems of Conservation Laws 1:Hyperbolicity, Entropies, Shock Waves  CAMBRIDGE UNIVERSITY PRESS  DENIS SERRE Translated by I . N. SNEDDON   Systems of Conservation Laws 1 Systems of conservation laws arise naturally in several areas of physics and chemistry. Tounderstand them and their consequences (shock waves, finite velocity wave propagation)properly in mathematical terms requires, however, knowledge of a broad range of topics.This book sets up the foundations of the modern theory of conservation laws describingthe physical models and mathematical methods, leading to the Glimm scheme. Buildingon this the author then takes the reader to the current state of knowledge in the subject. Inparticular, he studies in detail viscous approximations, paying special attention to viscousprofiles of shock waves. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation, whose convergence isstudied using the technique of compensated compactness. Small waves are studied usinggeometrical optics methods. Finally, the initial–boundary problem is considered in depth.Throughout, the presentation is reasonably self-contained, with large numbers of exercisesand full discussion of all the ideas. This will make it ideal as a text for graduate courses inthe area of partial differential equations. Denis Serre  is Professor of Mathematics at the Ecole Normale Sup´erieure de Lyon and wasa Member of the Institut Universitaire de France (1992–7).  This page intentionally left blank   Systems of Conservation Laws 1 Hyperbolicity, Entropies, Shock Waves DENIS SERRE Translated by I .  N .  SNEDDON
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