A Kernel-Density-Estimator Minimizing Movement Scheme for Diffusion Equations

Abstract

The mathematical theory of a novel variational approximation scheme for general second and fourth order partial differential equations \begin{equation}\label{eq: A} \partial_t u - \nabla\cdot\Big(u\nabla\frac{\delta\phi}{\delta u}(u)\Big|\nabla\frac{\delta\phi}{\delta u}(u)\Big|^{q-2}\Big) \ = \ 0, \quad\quad u\geq0, \end{equation} $q\in(1, +\infty)$, is developed.