Modeling Mass Transport in Aquifers: The Distributed SourceProblem

这是一个支持地下水污染物运动模拟研究的奖项。该项目的具体目标是设计一种方法，用于预测特定的主要污染物的移动，而不考虑其随机性质、浓度或在数学模型中的位置。此外，调查员正在考虑与污染物迁移有关的不确定来源，这些来源超出了可归因于含水层传导性的来源。他正在探索泛函分析理论的新基础(随机发展方程，算子半群，Hilbert空间中的随机微分方程)与经典热流方程的一些结果相结合，得到了受一般随机扰动的多孔介质中平流色散输运方程的新解。根据扰动随机过程在边界条件、源项和/或参数下的随机特性，该项目有望产生一种新的系统和通用的建模方法，用于预测集中过程的随机特性。此外，预计过程的方差不会像常规摄动技术那样被限制在小的幅度内。

This is an award to support research on modeling of the movement of groundwater pollutants. The specific objective of this project is to devise a methodology for prediction of the movement of a specific, principal contaminant regardless of its stochastic properties, concentration or location in the mathematical model. Additionally, the investigator is considering sources of uncertainty relative to contaminant migration beyond those attributable to aquifer conductivity. He is exploring new foundations in functional-analytic theory (stochastic evolution equations, semigroups of operators, stochastic differential equations in Hilbert space) blended with some results on the classical heat flow equation in order to obtain new solutions of the advective dispersive transport equation in porous media subject to a general stochastic disturbance. The project is expected to produce a new systematic and general modeling procedure by which the stochastic properties of the concentration process can be predicted based on the stochastic properties of the disturbing stochastic process(es) at the boundary conditions, the source terms and/or the parameters. Additionally, it is expected that the variances of the processes will not be restricted to small magnitudes as it is the case with conventional perturbation techniques.