Systems of conservation laws. 1, Hyperbolicity, entropies, shock waves / Denis Serre ; translated by I.N. Sneddon.

Format:

Book

Author/Creator:

Serre, D. (Denis), author.

Contributor:

Sneddon, Ian Naismith, translator.

Series:

Systems of conservation laws

Systems of conservation laws ; v. 1

Standardized Title:

Systèmes de lois de conservation. English

Language:

English

Subjects (All):

Conservation laws (Mathematics).

Physical Description:

1 online resource (xxii, 263 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 1999.

Language Note:

English

Summary:

Systems of conservation laws arise naturally in 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 conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

Contents:

Preliminaries; Contents; Acknowledgments; Introduction; 1 Some models; 2 Scalar equations in dimension d = 1; 3 Linear and quasi-linear systems; 4 Dimension d=D 1, the Riemann problem; 5 The Glimm scheme; 6 Second order perturbations; 7 Viscosity profiles for shock waves; Bibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-107-11393-8

1-280-41867-2

9786610418671

0-511-17247-8

0-511-15128-4

0-511-31055-2

0-511-61237-0

0-511-05397-5

OCLC:

437072430