Large time behavior and homogenization of solutions of two-dimensional conservation laws

1993 ◽  
Vol 46 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Bjorn Engquist ◽  
E Weinan
Keyword(s):  
Conservation Laws ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Two Dimensional

LARGE TIME BEHAVIOR OF NUMERICAL SOLUTIONS OF SCALAR CONSERVATION LAWS

2006 ◽  
Vol 03 (04) ◽  
pp. 631-648
Author(s):  
FRÉDÉRIC LAGOUTIÈRE
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Large Time ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Hyperbolic Conservation ◽  
Periodic Initial Data ◽  
Scalar Conservation

We study the large time behavior of entropic approximate solutions to one-dimensional, hyperbolic conservation laws with periodic initial data. Under mild assumptions on the numerical scheme, we prove the asymptotic convergence of the discrete solutions to a time- and space-periodic solution.

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