论文标题
侵蚀的数学模型和沉积物的最佳运输
Mathematical Models for Erosion and the Optimal Transportation of Sediment
论文作者
论文摘要
我们研究了沉积物侵蚀的数学理论，该理论始于对与扩展景观基本段相对应的矩形域上的非线性，抛物线加权的4-宽带方程的研究。施加自然的边界条件，我们表明该方程在存在时允许熵解决方案，并且证明了弱解的规律性和独特性。然后，我们研究了第一作者先前工作中研究的一类特定的弱解决方案，并对这些解决方案进行了数值模拟。在为沉积物流引入了最佳运输问题之后，我们表明，这类弱解决方案实现了沉积物的最佳运输。
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.
