Tuesday, 10 May 2016, 3 p.m. (sharp), Prof. Goro Akagi, Kobe University, at the conference room of IMATI-CNR in Pavia, will give a lecture titled:


as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.



This talk provides an overview of recent developments in a class of
gradient flows with strong irreversibility, which arise from Damage
Mechanics. We start with fully nonlinear forms and reduce them to
doubly nonlinear evolution equations having gradient structures. Main
purposes of analysis are to prove the well-posedness (mainly,
existence of solutions in an L^2-framework) and to investigate
qualitative properties of solutions (e.g., comparison principle) and
long-time behaviors of solutions (e.g., convergence to equilibrium or
blow-up in finite time of solutions). Methods of proof rely on energy
and variational techniques as well as approximations of equations
based on time-discretization or Moreau-Yosida approximations for
convex functionals. Furthermore, this class of equations also
motivates us to study infinite-dimensional dynamical systems strongly
depending on initial data: then the complete picture of such a
dynamical system could not be overviewed by focusing on the behavior
of the orbit emanating from each initial data. We also discuss a
couple of new attempts to investigate such a peculiar class of
dynamical systems.


Pagina web del Seminario di Matematica Applicata: