Seminario di equazioni differenziali e applicazioni: “A differential equation approach to implicit sweeping process”

Mercoledì 6 Febbraio 2019, ore 12:15 - Aula 1BC45 - Emilio Vilches


Mercoledì 6 Febbraio 2019 alle ore 12:15 in Aula 1BC45, Emilio Vilches (Universidad de O'Higgins, Cile) terrà un seminario dal titolo “A differential equation approach to implicit sweeping process”.

The sweeping process is a first-order differential inclusion involving normal cones to time-dependent moving sets which allows modeling several phenomena in contact mechanics, electric circuits, crowd motion, and hysteresis, among others. In this talk, we introduce and study an implicit version of the sweeping process. Based on the methods of convex analysis, we show the equivalence of the implicit sweeping process with a differential equation, which enables us to prove its existence and uniqueness in a very general framework. The existence results are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.

[1] A. Jourani, E. Vilches: A differential equation approach to implicit sweeping processes, J. differential
Equations (In press), 2018.

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