Gradient flows with strong irreversibility
Prof. Goro Akagi, Kobe University
Sala Conferenze, IMATI-CNR - Tuesday, May 10, 2016 h.15:00
Abstract. 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 L2-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.
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