Wednesday, October 19, 2022 - 14:00 in V3-201 + Zoom
The Trotter product formula for nonlinear Fokker-Planck flows
A talk in the Bielefeld Stochastic Afternoon series by
Viorel Barbu
| Abstract: |
The nonlinear Fokker-Planck flow $S(t)$ in $L^1$ generated by the equation
\begin{align*}
\rho_t - \Delta \beta (\rho) + \text{div} (a(\rho)\rho) = 0, \quad \rho(0) = \rho_0
\end{align*}
can be expressed by the Trotter-Lie formula
\begin{align*}
S(t) \rho_0 = \lim_{n \to \infty} (S_1 (\frac{t}{n}) S_2(\frac{t}{n}))^n \rho_0 \quad \text{ in } L^1(\mathbb{R}^d),
\end{align*}
where $S_1$ is the semigroup generated by $\rho \rightarrow - \Delta \beta(\rho)$ and $S_2(t)$ that generated by $\rho \rightarrow \text{div}(a(\rho)\rho)$ (in entropy solution sense).
Within the CRC this talk is associated to the project(s): A5, B1 |
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