The $l^1$ global decay to discrete shocks for scalar monotone schemes
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Abstract:
Given a family of discrete shocks $\phi$ of a monotone scheme, we prove that the discrete shock profile with rational shock speed $\eta$ is asymptotically stable with respect to the $l^1$ topology $\|\cdot \|_1$: if $u^0-\phi \in l^1$, then $\|u^n -\phi _{\cdot - n\eta }\|_1 \to 0$ as $n\to \infty$ under no restriction conditions of the initial data to the interval $[\inf \phi , \sup \phi ]$. The asymptotic wave profile is uniquely identified from the above family by a mass parameter.References
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Additional Information
- Hailiang Liu
- Affiliation: UCLA, Mathematics Department, Los Angeles, California 90095-1555
- Email: hliu@math.ucla.edu
- Received by editor(s): December 13, 1999
- Received by editor(s) in revised form: November 16, 2000, and January 3, 2001
- Published electronically: September 17, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 227-245
- MSC (2000): Primary 35L65, 65M06, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-01-01380-1
- MathSciNet review: 1933819