Dynamics in the fundamental solution of a non-convex conservation law
2015 ◽
Vol 146
(1)
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pp. 169-193
Keyword(s):
There is a huge jump in the theory of conservation laws if the convexity assumption is dropped. We study a scalar conservation law without the convexity assumption by monitoring the dynamics in the fundamental solution. We introduce three shock types in addition to the usual genuine shock: left-, right- and double-sided contacts. There are three kinds of phenomenon for these shocks, called branching, merging and transforming. All of these shocks and phenomena can be observed if the flux function has two inflection points. A comprehensive picture of a global dynamics of a non-convex flux is discussed in terms of characteristic maps and dynamical convex–concave envelopes.
2019 ◽
Vol 11
(1)
◽
pp. 46-60
Keyword(s):
2012 ◽
Vol 64
(4)
◽
pp. 1025-1056
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2003 ◽
Vol 13
(02)
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pp. 221-257
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2000 ◽
Vol 171
(1)
◽
pp. 15-33
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2009 ◽
Vol 2009
◽
pp. 1-33
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2005 ◽
Vol 43
(2)
◽
pp. 559-577
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2013 ◽
Vol 20
(2)
◽
pp. 229-244
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2001 ◽
Vol 45
(8)
◽
pp. 1039-1060
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2011 ◽
Vol 235
(18)
◽
pp. 5394-5410
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Keyword(s):
2003 ◽
Vol 52
(1)
◽
pp. 227-256
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