ON EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTIONS TO THE CAUCHY PROBLEM FOR A CONSERVATION LAW WITH DISCONTINUOUS FLUX
2009 ◽
Vol 06
(03)
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pp. 525-548
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Keyword(s):
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.
2003 ◽
pp. 789-796
Keyword(s):
Keyword(s):
1999 ◽
Vol 63
(1)
◽
pp. 129-179
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1994 ◽
Vol 13
(3)
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pp. 477-491
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1992 ◽
Vol 23
(3)
◽
pp. 635-648
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Keyword(s):
2008 ◽
Vol 150
(6)
◽
pp. 2578-2587
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Keyword(s):
2002 ◽
Vol 66
(6)
◽
pp. 1171-1218
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Keyword(s):
2000 ◽
Vol 191
(1)
◽
pp. 121-150
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Keyword(s):
2002 ◽
Vol 193
(5)
◽
pp. 727-743
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Keyword(s):