| Abstract: |
| In this talk, I will deal with a class of nonlinear Fokker-Planck equations with the following structure:
\begin{equation}
\partial_t u - \text{div}\big(M\nabla u+ E h(u)\big)=0,
\end{equation}
where $M$ is a bounded elliptic matrix, $E$ is a vector field in a suitable Lebesgue space, and $h(u)$ exhibits a superlinear growth.
I will provide existence results for $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the above equation under general assumptions on the coefficients. The approach followed is entirely non-variational, does not require specific structural assumptions on the vector field $E$ (such as being a gradient), and avoids the use of representation formulas.
Additionally, some qualitative properties of the solutions will be discussed. These results have been obtained in collaboration with Stefano Buccheri and Fernando Farroni. |
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