Chapter 7 L1-stability of nonlinear waves in scalar conservation laws

2002 ◽  
pp. 473-553 ◽  
Author(s):  
Denis Serre
Keyword(s):  
Conservation Laws ◽  
Nonlinear Waves ◽  
Scalar Conservation Laws ◽  
L1 Stability ◽  
Scalar Conservation

scholarly journals Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

2009 ◽  
Vol 2009 ◽  
pp. 1-26 ◽  
Author(s):  
V. G. Danilov ◽  
D. Mitrovic
Keyword(s):  
Approximate Solution ◽  
Initial Data ◽  
Conservation Laws ◽  
Asymptotic Method ◽  
Nonlinear Waves ◽  
Conservation Law ◽  
Scalar Conservation Laws ◽  
Scalar Conservation Law ◽  
Scalar Conservation ◽  
Smooth Approximations

We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.

scholarly journals Numerical Solution of Scalar Conservation Laws with Random Flux Functions

2016 ◽  
Vol 4 (1) ◽  
pp. 552-591 ◽  
Author(s):  
Siddhartha Mishra ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Svetlana Tokareva
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Scalar Conservation Laws ◽  
Scalar Conservation
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