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Seminario di Equazioni Differenziali e Applicazioni
Venerdì 19 Giugno 2015 alle ore 12:15 in Aula 2AB40, Laura Caravenna (Università di Padova) terrà un seminario dal titolo "A counter-example concerning regularity properties for systems of conservation laws".
In 1973 Schaeffer established a result that applies to scalar conservation laws with convex fluxes and which can be roughly speaking formulated as follows: for a generic smooth initial datum, the admissible solution is smooth outside a locally finite number of curves in the time-space plane. Here the term "generic" should be interpreted in a suitable topological sense, related to the Baire Category Theorem. My talk will aim at discussing a recent explicit mathematical counter-example that shows that Schaffer's Theorem does not extend to nonlinear hyperbolic systems of conservation laws. I will also mention related problems.
The talk will be mainly based on joint works with Laura Spinolo.
Rif. Int. M. Bardi, C. Marchi, G. Colombo