TY - RPRT
T1 - On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension
Y1 - 2016
A1 - Stefano Bianchini
A1 - Elio Marconi
AB - 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 counterexamples which show that these results are sharp.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/35209
U1 - 35508
U2 - Mathematics
U5 - MAT/05
ER -