Systems of Conservation Laws 2: Geometric Structures, Oscillations, and Initial-Boundary Value Problems - Hardcover

Serre, Denis

Hardcover

ISBN 10: 0521633303 ISBN 13: 9780521633307

Publisher: Cambridge University Press, 2000

Synopsis

Systems of conservation laws arise naturally in physics and chemistry. Continuing where the previous volume left off, the author considers the maximum principle from the viewpoints of both viscous approximation and numerical schemes. Convergence is studied through compensated compactness. The author applies this tool to the description of large amplitude wave propagation. Small waves are studied through geometrical optics. Special structures are presented in chapters on rich and Temple systems. Finally, Serre explains why the initial-boundary value problem is far from trivial, with descriptions of the Kreiss-Lopatinski condition for well-posedness, with applications to shock wave stability, and certain problems in boundary layer theory. 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.

About this title

Book Description:

Systems of conservation laws arise naturally in physics and chemistry. Following on from the previous volume, Serre looks at more advanced topics, e.g. the maximum principle and geometrical ideas, and studies in detail their application to shock wave stability, and certain problems in boundary layer theory.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.

Review:

'... an exciting book ... this book can be seriously recommended for mathematicians working in the modern fields under question ... treats the development of recent years exhaustively.' R. Ansorge, ZAMM

'... presents ideas on the cutting edge of research ... The reader ... will find a fascinating array of new tools being brought to bear on nonlinear HPDEs.' T. J. Bridges, Contemporary Physics

About this edition

• Publisher: Cambridge University Press
• Publication date: 2000
• ISBN 10: 0521633303
• ISBN 13: 9780521633307
• Binding: Hardcover
• Number of pages: 282