Fractional BV spaces and applications to scalar conservation laws
2014 ◽
Vol 11
(04)
◽
pp. 655-677
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Keyword(s):
We obtain new fine properties of entropy solutions to scalar nonlinear conservation laws. For this purpose, we study the "fractional BV spaces" denoted by BVs(ℝ) (for 0 < s ≤ 1), which were introduced by Love and Young in 1937 and closely related to the critical Sobolev space Ws,1/s(ℝ). We investigate these spaces in connection with one-dimensional scalar conservation laws. The BVs spaces allow one to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with BVs initial data. Furthermore, for the first time, we get the maximal Ws,p smoothing effect conjectured by Lions, Perthame and Tadmor for all nonlinear (possibly degenerate) convex fluxes.
2017 ◽
Vol 451
(2)
◽
pp. 712-735
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Keyword(s):
2017 ◽
Vol 62
(4)
◽
pp. 1620-1635
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1998 ◽
Vol 15
(2)
◽
pp. 169-190
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Keyword(s):
2011 ◽
Vol 46
(1)
◽
pp. 498-504
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2009 ◽
Vol 228
(14)
◽
pp. 5298-5315
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Keyword(s):
1998 ◽
Vol 148
(2)
◽
pp. 292-317
◽
2000 ◽
Vol 38
(3)
◽
pp. 964-988
◽
2012 ◽
Vol 09
(04)
◽
pp. 571-611
◽
1993 ◽
Vol 18
(9-10)
◽
pp. 1631-1652
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