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A Kernel-Density-Estimator Minimizing Movement Scheme for Diffusion Equations (2310.11961v1)
Published 18 Oct 2023 in math.AP, cs.NA, and math.NA
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.