scholarly journals Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

2019 ◽  
Vol 7 (3) ◽  
pp. 806-837
Author(s):  
James M. Scott ◽  
M. Paul Laiu ◽  
Cory D. Hauck
Keyword(s):  
Initial Data ◽  
Balance Laws ◽  
Random Initial Data ◽  
Hyperbolic Balance Laws

N-WAVES IN HYPERBOLIC BALANCE LAWS

2012 ◽  
Vol 09 (02) ◽  
pp. 339-354 ◽  
Author(s):  
CONSTANTINE M. DAFERMOS
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Compact Support ◽  
Balance Laws ◽  
Hyperbolic Balance Laws ◽  
The Cauchy Problem ◽  
Wave Profiles ◽  
N Wave

It is shown that, as time tends to infinity, solutions to the Cauchy problem for a class of genuinely nonlinear scalar balance laws attain N-wave profiles, when the initial data have compact support, or saw-toothed profiles, when the initial data are periodic. The amplitude and length of these waves results from the synergy between flux and source.

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