Hyperbolic Systems of Balance Laws in One-Space Dimension

2009 ◽  
pp. 195-229
Author(s):  
Constantine M. Dafermos
Keyword(s):  
Space Dimension ◽  
Hyperbolic Systems ◽  
Balance Laws ◽  
Systems Of Balance Laws ◽  
One Space Dimension

Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation

2015 ◽  
Vol 12 (02) ◽  
pp. 277-292 ◽  
Author(s):  
Constantine M. Dafermos
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Total Variation ◽  
Space Dimension ◽  
Hyperbolic Systems ◽  
Relaxation Processes ◽  
Balance Laws ◽  
Type Condition ◽  
Systems Of Balance Laws ◽  
The Cauchy Problem

For hyperbolic systems of balance laws governing relaxation processes, in one space dimension, with source incurring nonnegative entropy production and satisfying a Kawashima-type condition, it is shown that when the initial data have small total variation on (-∞, ∞) and decay rapidly to zero, as |x| → ∞, then the Cauchy problem possesses a unique admissible BV solution, in the large, with total variation decaying to zero, as t → ∞.

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