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Seminario di Equazioni Differenziali e Applicazioni: Scalar conservation laws with discontinuous flux

Martedì 8 Marzo 2016, ore 12:00 - Aula 2BC30 - Francesco Ghiraldin

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Martedì 8 Marzo 2016 alle ore 12:00 in Aula 2BC30 Francesco Ghiraldin (Max Planck Institute Leipzig) terrà un seminario dal titolo "Scalar conservation laws with discontinuous flux".

Abstract
In the talk I will investigate the uniqueness of solutions of scalar conservation laws with discontinuous flux. While in the smooth setting this property follows from Kruzhkov's entropy inequalities, in the case of discontinuous fluxes these inequalities are not enough and additional dissipation conditions must be imposed at the discontinuity set of the flux. I will explain how any entropy solution admits traces on the discontinuity set of the flux field and use this to prove the validity of a generalized Kato inequality for any pair of solutions. Applications to uniqueness of solutions will then be given.

Rif. Int. M. Bardi, C. Marchi, L. Caravenna

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