The global decay to discrete shocks for scalar monotone schemes

Author:
Hailiang Liu

Journal:
Math. Comp. **72** (2003), 227-245

MSC (2000):
Primary 35L65, 65M06, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-01-01380-1

Published electronically:
September 17, 2001

MathSciNet review:
1933819

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a family of discrete shocks of a monotone scheme, we prove that the discrete shock profile with rational shock speed is asymptotically stable with respect to the topology : if , then as under no restriction conditions of the initial data to the interval . The asymptotic wave profile is uniquely identified from the above family by a mass parameter.

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Additional Information

**Hailiang Liu**

Affiliation:
UCLA, Mathematics Department, Los Angeles, California 90095-1555

Email:
hliu@math.ucla.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01380-1

Keywords:
$l^1$ decay,
discrete shocks,
monotone scheme

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

Article copyright:
© Copyright 2001
American Mathematical Society