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

A graduate text on mathematical theory of conservation laws and partial differential equations.

Denis Serre (Author), I. N. Sneddon (Translated by)

9780521633307, Cambridge University Press

Hardback, published 3 February 2000

282 pages, 4 b/w illus. 56 exercises
24.4 x 17 x 1.7 cm, 0.64 kg

'… 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

Systems of conservation laws arise naturally in physics and chemistry. Following on from the previous volume, the author considers the maximum principle from the viewpoints of both viscous approximation and numerical schemes. Convergence is studied through compensated compactness. This tool is applied 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.

8. The maximum principle
9. Compensated compactness
10. Propagation of oscillations
11. Weakly nonlinear geometric optics
12. Rich systems
13. Temple fields and systems
14. Boundary conditions and mixed problems
15. Boundary layers
Bibliography
Index.

Subject Areas: Applied mathematics [PBW], Calculus & mathematical analysis [PBK]