We show that the continuum shock profiles for dissipative difference schemes constructed in Part I are nonlinearly stable. It is shown first that the profiles have the conservation property, obtained as the limit of the discrete version for profiles with nearby rational, quasi-Diophantine speeds. Th
Semi-discrete shock profiles for hyperbolic systems of conservation laws
โ Scribed by S. Benzoni-Gavage
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 567 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0167-2789
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โฆ Synopsis
The existence of semi-discrete shock profiles for a general hyperbolic system of conservation laws is proved. Such profiles are regarded as heteroclinic orbits of a retarded functional differential equation (RFDE). The proof relies on the Hale center manifold theorem and holds for shocks of small strength.
๐ SIMILAR VOLUMES
We construct continuum shock profiles for finite difference schemes for hyperbolic conservation laws. Our analysis is based on the time-asymptotic estimates for solutions of the difference schemes. Our result applies to dissipative schemes with the nonresonance property, such as the Lax-Friedrichs a