Mathematical Models for Erosion and the Optimal Transportation of Sediment
Abstract
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment.
Keywords
Cite
@article{arxiv.2012.07736,
title = {Mathematical Models for Erosion and the Optimal Transportation of Sediment},
author = {Björn Birnir and Julie Rowlett},
journal= {arXiv preprint arXiv:2012.07736},
year = {2020}
}
Comments
This was published in the International Journal of Nonlinear Sciences and Numerical Simulation in 2013. According to the publisher's policies, after 12 months, the article can be made available here!