Existence of weak solutions to a continuity equation with space time nonlocal Darcy law
Analysis of PDEs
2020-08-19 v7
Abstract
In this manuscript we consider a porous medium equation with non-local diffusion effects given by a fractional heat operator in two space dimensions. Global in time existence of weak solutions is shown by employing a time semi-discretization of the equations, an energy inequality, a higher order integral estimate, and a generalized version of the Div-Curl lemma.
Keywords
Cite
@article{arxiv.1805.08666,
title = {Existence of weak solutions to a continuity equation with space time nonlocal Darcy law},
author = {Luis Caffarelli and Maria Gualdani and Nicola Zamponi},
journal= {arXiv preprint arXiv:1805.08666},
year = {2020}
}