Special Session 99: Emerging Trends in Analysis and Control of PDEs

Null controllability for a degenerate Fokker-Plank equation with a drift term
GENNI FRAGNELLI
University of Siena
Italy
Co-Author(s):    Dimitri Mugnai
Abstract:
The Fokker-Planck equation describes the time evolution of the probability density function of the velocity for a particle under the influence of drag forces and random forces. In particular, this equation has multiple applications in information theory, graph theory, data science, finance, economics... In one spatial dimension the Fokker-Planck equation for the probability density $p(t,x)$ can be rewritten as \[ p_t(t,x) - (a(t,x)p(t.x))_{xx} + (\mu(t,x)p(t,x))_x= f(t,x) \] where $t\in [0, T]$, $T>$ is fixed and $x \in (0,1)$. In this talk we assume that $a$ is a function degenerating at $x=0$; the purpose is to study the null-controllability of the solution, namely the possibility to drive the solution $p$ to rest completely at time $T$.