Wednesday, August 9, 2023 - 15:30 in V3-201 + Zoom
The nonlinear Fokker-Planck equation as a smooth gradient flow
A talk in the Bielefeld Stochastic Afternoon series by
Viorel Barbu
| Abstract: |
Based on the $H^{-1}$ regularity of the semigroup
$S(t):[0,\infty) \rightarrow L^1(R^d))$ associated with the
Fokker-Planck equation
$$u_t -\Delta \beta(u) + div(D b(u)u) = 0 in (0,\infty \times R^d).$$
Here one improves a recent result of M.Rehmeier and M. Rockner
regarding the corresponding gradient flow
$$d/dt u(t) = -\nabla E_{u(t)} a.e. t>0$$
where $u(t) =S(t)u_0.$
Namely, one shows that the above gradient flow equation holds
everywhere on $(0, \infty) \, N$ where N is a countable set and with
$d^{+} /dt$ everywhere on $(0, \infty)$.
Within the CRC this talk is associated to the project(s): A5 |
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