On the Structure of $${L^\infty}$$ -Entropy Solutions to Scalar Conservation Laws in One-Space Dimension
Tóm tắt
We prove that if u is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular, the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a C
0-sense up to the degeneracy due to the segments where
$${f''=0}$$
. We prove also that the initial data is taken in a suitably strong sense and we give some examples which show that these results are sharp.
Tài liệu tham khảo
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