dear all
this is to announce that Theodore Drivas (Princeton University) will
give a talk on
*next Wednesday, June 12*
at 11am in Sala Seminari, Dipartimento di Matematica, Università di Pisa
(largo B. Pontecorvo 5, 56127 Pisa).
cheers
m.
*Title*: /Spontaneously stochastic solutions in dynamical systems with
singularities/
*Abstract*: We consider a class of dynamical systems described by
ordinary differential equations with an isolated singularity, where the
singularity is characterized by the lack of Lipschitz continuity.
Singularities are common in applications both for ODEs (e.g., particles
collisions) and PDEs (e.g., finite-time blowup in fluid models). The
fundamental obstacle is that solutions cannot be continued past the
singularity uniquely: typically, there are infinitely many solutions.
The conventional way to proceed is to define a regularization limit,
such as vanishing viscosity or noise. It turns out that there are
structurally stable situations when such a limit is not sensitive to a
particular form of the regularization. This is explained by the analysis
of attractors for the rescaled (non-singular) dynamical system and their
ergodic properties. What is even more surprising is that solutions in
this limit may become probabilistic (spontaneously stochastic) with the
unique probability measure past the singularity. We will present
rigorous results and discuss applications of this phenomenon.