# Seminari di Equazioni Differenziali e Applicazioni: “Conservation laws with discontinuous flux: backward Euler approximations and regulated fluxes”

## Mercoledì 21 Marzo 2018, ore 14:30 - Aula 2BC30 - Graziano Guerra

ARGOMENTI: Seminari

Mercoledì 21 Marzo 2018 alle ore 14:30 in Aula 2BC30, Graziano Guerra (Università di Milano - Bicocca) terrà un seminario dal titolo “Conservation laws with discontinuous flux: backward Euler approximations and regulated fluxes”.

Abstract
Scalar conservation laws with the flux discontinuous with respect to the time--space variables arise in many applications where the conservation laws describe physical models in rough media. We are interested in solutions to these type of equations obtained using vanishing viscosity approximations.
We show that the Crandall Liggett theory of nonlinear semigroup provides a very elegant framework for proving the existence and the uniqueness of the vanishing viscosity limit when the flux has a single discontinuity at the origin. Some examples and counterexamples are given. Then we give a definition of regulated functions in two variables which generalizes the definition of functions with bounded total variation and we show the existence and uniqueness of the vanishing viscosity limit for regulated fluxes.