scholarly journals A kinetic equation with kinetic entropy functions for scalar conservation laws

1991 ◽  
Vol 136 (3) ◽  
pp. 501-517 ◽  
Author(s):  
Benoit Perthame ◽  
Eitan Tadmor
Keyword(s):  
Kinetic Equation ◽  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
Scalar Conservation ◽  
Entropy Functions

HIGH-FIELD LIMIT FROM A KINETIC EQUATION TO MULTIDIMENSIONAL SCALAR CONSERVATION LAWS

2007 ◽  
Vol 04 (01) ◽  
pp. 123-145 ◽  
Author(s):  
F. BERTHELIN ◽  
N. J. MAUSER ◽  
F. POUPAUD
Keyword(s):  
Kinetic Equation ◽  
Conservation Laws ◽  
High Field ◽  
Distribution Functions ◽  
Scalar Conservation Laws ◽  
Field Limit ◽  
Flux Function ◽  
Transport Operator ◽  
Scalar Conservation

We study the relaxation of kinetic BGK models involving a high-field term within the transport operator. They lead us to multidimensional scalar conservation laws with a flux-function which is perturbed with respect to classical relaxation. The proof of the relaxation limit makes modified Maxwellians to appear. We consider "pseudo distribution functions" which can take negative values and we introduce appropriate admissible states. This is a first step towards adapting this analysis to quantum kinetic BGK models.

Transport-collapse scheme for heterogeneous scalar conservation laws

2018 ◽  
Vol 15 (01) ◽  
pp. 119-132
Author(s):  
Darko Mitrović ◽  
Andrej Novak
Keyword(s):  
Cauchy Problem ◽  
Kinetic Equation ◽  
Conservation Laws ◽  
Admissible Solution ◽  
Scalar Conservation Laws ◽  
Numerical Examples ◽  
The Cauchy Problem ◽  
Scalar Conservation

We extend Brenier’s transport collapse scheme on the Cauchy problem for heterogeneous scalar conservation laws i.e. for the conservation laws with spacetime-dependent coefficients. The method is based on averaging out the solution to the corresponding kinetic equation, and it necessarily converges toward the entropy admissible solution. We also provide numerical examples.

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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