STRUCTURE OF ENTROPY SOLUTIONS TO SCALAR CONSERVATION LAWS WITH STRICTLY CONVEX FLUX
2012 ◽
Vol 09
(04)
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pp. 571-611
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Keyword(s):
We consider scalar conservation laws in one space dimension with convex flux and we establish a new structure theorem for entropy solutions by identifying certain shock regions of interest, each of them representing a single shock wave at infinity. Using this theorem, we construct a smooth initial data with compact support for which the solution exhibits infinitely many shock waves asymptotically in time. Our proof relies on Lax–Oleinik explicit formula and the notion of generalized characteristics introduced by Dafermos.
2017 ◽
Vol 226
(1)
◽
pp. 441-493
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2015 ◽
Vol 428
(1)
◽
pp. 356-386
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2007 ◽
Vol 04
(03)
◽
pp. 369-389
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Keyword(s):
2017 ◽
Vol 63
(3)
◽
pp. 418-436
2017 ◽
Vol 62
(4)
◽
pp. 1620-1635
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1998 ◽
Vol 15
(2)
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pp. 169-190
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Keyword(s):
2018 ◽
Vol 50
(3)
◽
pp. 3122-3146
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2017 ◽
Vol 451
(2)
◽
pp. 712-735
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Keyword(s):
2014 ◽
Vol 11
(04)
◽
pp. 655-677
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