Calculus of Variations and Geometric Measure Theory
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Scalar conservation laws with discontinuous flux

Francesco Ghiraldin (Max Planck Institute Leipzig)

created by gelli on 23 Apr 2017

3 may 2017 -- 17:00   [open in google calendar]

Sala seminari (Dipartimento di Matematica di Pisa)

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.

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