scholarly journals Solution of the Cauchy Problem for a Conservation Law with a Discontinuous Flux Function

1992 ◽  
Vol 23 (3) ◽  
pp. 635-648 ◽  
Author(s):  
Tore Gimse ◽  
Nils Henrik Risebro
Keyword(s):  
Cauchy Problem ◽  
Conservation Law ◽  
Flux Function ◽  
Discontinuous Flux Function ◽  
The Cauchy Problem ◽  
Discontinuous Flux

ON EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTIONS TO THE CAUCHY PROBLEM FOR A CONSERVATION LAW WITH DISCONTINUOUS FLUX

2009 ◽  
Vol 06 (03) ◽  
pp. 525-548 ◽  
Author(s):  
E. YU. PANOV
Keyword(s):  
Cauchy Problem ◽  
Unknown Function ◽  
Conservation Law ◽  
Existence And Uniqueness ◽  
Entropy Solutions ◽  
Generalized Entropy ◽  
The Cauchy Problem ◽  
Discontinuous Flux

We study the Cauchy problem for a conservation law with space discontinuous flux of generalized Audusse–Perthame form. It is shown that, after a change of unknown function, entropy solutions in the sense of Audusse–Perthame correspond to Kruzhkov's generalized entropy solutions for the transformed equation. This observation allows to use the Kruzhkov method of doubling variable (instead of rather complicated variant of this method invented by Audusse and Perthame). Applying this method for measure-valued solutions, we establish the uniqueness and the existence of entropy solutions to the problem under consideration.

scholarly journals Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function

2009 ◽  
Vol 2009 ◽  
pp. 1-33 ◽  
Author(s):  
H. Holden ◽  
K. H. Karlsen ◽  
D. Mitrovic
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Flux Function ◽  
Discontinuous Flux Function ◽  
Scalar Conservation Law ◽  
Discontinuous Flux ◽  
Dispersion Terms ◽  
Scalar Conservation

We consider multidimensional conservation laws with discontinuous flux, which are regularized with vanishing diffusion and dispersion terms and with smoothing of the flux discontinuities. We use the approach ofH-measures to investigate the zero diffusion-dispersion-smoothing limit.

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