Personal tools

Theme for TIFR Centre For Applicable Mathematics, Bangalore

You are here: Home / On the structure of $$L^\infty$$-entropy solutions to scalar conservation laws in one-space dimension

# On the structure of $$L^\infty$$-entropy solutions to scalar conservation laws in one-space dimension

Prof. Stefano Bianchini SISSA, Trieste, Italy
 Speaker Prof. Stefano Bianchini SISSA, Trieste, Italy Dec 12, 2017 from 11:30 AM to 12:30 PM LH 006 vCal iCal

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.

Filed under: