Wednesday, January 28, 2026 - 14:00 in V3-201+Zoom
The Leibenson as a nonlinear Fokker--Planck equation and its associated nonlinear Markov process
A talk in the Bielefeld Stochastic Afternoon series by
Marco Rehmeier
| Abstract: |
We prove that the Barenblatt solutions of the Leibenson equation
\begin{equation*}
\partial_t u(t,x) = \Delta_p u^q(t,x),\quad (t,x) \in (0,\infty) \times R^d
\end{equation*}
(also called doubly nonlinear evolution equation), where $\Delta_p f = \div(|\nabla f|^{p-2}\nabla f)$ denotes the $p$-Laplace operator,
are the one-dimensional time marginals of a weak solution to a McKean--Vlasov equation whose coefficients depend on the solution law pointwise via the gradient of its density. To this end, we first identify the Leibenson equation as a nonlinear Fokker--Planck equation. Moreover, we prove that the Barenblatt solutions determine a unique nonlinear Markov process, which we call the Leibenson process. This is joint work with Viorel Barbu, Sebastian Grube and Michael Röckner.
Within the CRC this talk is associated to the project(s): A5 |
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