Speaker
Genni Fragnelli
(Università di Siena)
Description
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 $T$.
Author
Genni Fragnelli
(Università di Siena)