Convergence rate of approximate solutions to weakly coupled nonlinear systems

Author:
Haim Nessyahu

Journal:
Math. Comp. **65** (1996), 575-586

MSC (1991):
Primary 35L65; Secondary 65M10, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-96-00716-8

MathSciNet review:
1333321

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the convergence rate of approximate solutions to nonlinear hyperbolic systems which are weakly coupled through linear source terms. Such weakly coupled systems appear, for example, in the context of resonant waves in gas dynamics equations.

This work is an extension of our previous scalar analysis. This analysis asserts that a One Sided Lipschitz Condition (OSLC, or -stability) together with -consistency imply convergence to the unique entropy solution. Moreover, it provides sharp convergence *rate* estimates, both global (quantified in terms of the -norms) and local.

We focus our attention on the -stability of the viscosity regularization associated with such weakly coupled systems. We derive sufficient conditions, interesting for their own sake, under which the viscosity (and hence the entropy) solutions are -stable in an appropriate sense. Equipped with this, we may apply the abovementioned convergence rate analysis to approximate solutions that share this type of -stability.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-96-00716-8

Received by editor(s):
May 24, 1993

Additional Notes:
This research was supported in part by the Basic Research Foundation, Israel Academy of Sciences and Humanities

$^{1}$ Passed away in the dawn of April the 26th, 1994, at age 29, in The Himalayas, Nepal

Article copyright:
© Copyright 1996
American Mathematical Society