Geometric structures, oscillations, and initial-boundary value problems
著者
書誌事項
Geometric structures, oscillations, and initial-boundary value problems
（Systems of conservation laws / Denis Serre, 2）
Cambridge University Press, 2000
- : hbk
- タイトル別名
-
Structures géométriques, oscillations et problèmes mixtes
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注記
Originally published in French under the title: Systèmes de lois de conservation 2: structures géométriques, oscillations et problèmes mixtes, by Diderot, c1996
Bibliography: p. 261-265
Includes Index
内容説明・目次
内容説明
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.
目次
- 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.
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