Surprise and predictability in bounded sources of non-convex balance laws

 Laura Caravenna (Padova, Italy)

In the talk I will show surprising and predictable aspects of bounded source terms in a non-convex balance law, with smooth flux,
when it admits a continuous solution. Namely, I will discuss to what extent the conservation law can be reduced to an (infinitely dimensional) system of ODEs along the characteristic curves. This correspondence is evident in the classical setting but it is surprising in this context with lack of regularity. Part of the correspondence just requires suitable definitions and smart technicality, but concerning part of it new odd unexpected behaviors show up. The presentation is mostly based on a joint work with S. Bianchini (SISSA) and G. Alberti (Pisa), and it extends previous works by several authors relative to the case of the quadratic flux.

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