A variational approach to rate-independent problems (5 lectures)

Giuseppe Savaré

(Università di Pavia)

Date: Jun 13, 2011

Place: Padova

Minicourses of Mathematical Analysis

Abstract. The course will present a concise overview of the variational theory for rate-independent pro-
cesses. Starting from some basic examples, we will discuss the link with gradient
ows and
doubly-nonlinear di erential equations in Hilbert/Banach spaces. The method of incremental
minimizations and Mielke's "Energetic formulation" will be considered and compared with the
recent notion of "BV-solution" related to viscous approximation. Some general existence, ap-
proximation, and stability results will be derived, with applications to various kind of models
governed by ordinary or partial di erential equations.