On the structure of \(L^\infty\)entropy solutions to scalar conservation laws in onespace dimension
Speaker 
Prof. Stefano Bianchini SISSA, Trieste, Italy


When 
Dec 12, 2017
from 11:30 AM to 12:30 PM 
Where  LH 006 
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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 1rectifiable 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.