Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

$ L\sp 1$-stability of stationary discrete shocks


Authors: Jian-Guo Liu and Zhou Ping Xin
Journal: Math. Comp. 60 (1993), 233-244
MSC: Primary 35L65; Secondary 35L67, 65M12
MathSciNet review: 1159170
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The nonlinear stability in the $ {L^p}$-norm, $ p \geq 1$, of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general $ m \times m$ systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 35L65, 35L67, 65M12

Retrieve articles in all journals with MSC: 35L65, 35L67, 65M12


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1159170-7
PII: S 0025-5718(1993)1159170-7
Keywords: Lax-Friedrichs scheme, hyperbolic systems of conservation laws, discrete shock profiles, nonlinear stability
Article copyright: © Copyright 1993 American Mathematical Society