Seminar Analysis: Laura Caravenna (Università degli Studi di Padova)

Eulerian and Lagrangian continuous solutions to a non-convex balance law

We consider continuous solutions to the single balance law ∂_tu+∂_x(f(u)) = g, g bounded, f ∈ C². We discuss correspondences among the source terms in the Eulerian and Lagrangian settings, extending previous works relative to the flux f(u) = u² when possible. Counterexamples point out a new behavior of solutions when f is non-convex, and when the set of inflection points of f is not negligible, stressing the difference among the Lagrangian/Eulerian formulations in this context. 

This is a joint work with G. Alberti and S. Bianchini. 

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