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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

Transcript

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).
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Systems of Conservation Laws 1
Hyperbolicity, Entropies, Shock Waves
DENIS SERRE
Translated by
I
.
N
.
SNEDDON

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