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| LARGE TIME STEP GENERALIZATIONS OF GLIMM'S SCHEME FOR SYSTEMS OF CONSERVATION LAWS |
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Citation： |
Wang Jinghua.LARGE TIME STEP GENERALIZATIONS OF GLIMM'S SCHEME FOR SYSTEMS OF CONSERVATION LAWS[J].Chinese Annals of Mathematics B,1988,9(4):456~469 |
| Page view： 779
Net amount： 817 |
Authors： |
Wang Jinghua; |
Foundation： |
The Project Supported by National Science Foundation of China. |
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| Abstract： |
Two kinds of generalizations of Glimin's scheme for Courant numbers larger than 1/2 is introduced For one kind of the generalizations, referred to as L.T. S. Glimm's scheme(I), it is shown that for any fixed(but arbitrary la rge） Courant number if a sequence of:
approximate solutions converges to a limit u as the mesh is refined then u is a werk solution to the system of conservation laws for almost choise of random sequence. Further more it is obtained that for scalar equations and systems of conservation laws the family of approximate solutions contains convergent subsequence.
For another kind of generalizations with any fixed (but arbitrary large) Courant number, referred to as L. T. S. Glimm's scheme(II), it is proved that the family of
approximate solutions to the system of isothermal gas dynamics equations contains a convergent subsequence provided the total variation of the initial data is bounded. |
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