应用数学青年讨论班(午餐会)--Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control
报告人：李怡群（武汉大学）
时间：2026-05-13 12:00-13:30
地点：智华楼四元厅
摘要：
We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in petroleum reservoir simulation or groundwater contaminant transport. Specifically, we incorporate the no-flux boundary condition for the Darcy velocity to prove that the general no-flux boundary condition for the transport equation is equivalent to the normal derivative boundary condition of the concentration, based on which we further prove several complex boundary conditions by the Bear-Scheidegger tensor and its derivative. The derived boundary conditions not only provide new insights and distinct properties of the Bear-Scheidegger diffusion-dispersion tensor, but accommodate the coupling and the nonlinearity of the miscible displacement system and the Bear-Scheidegger tensor in deriving the first-order optimality condition of the corresponding optimal control problem for practical application.
报告人简介：
李怡群博士毕业于University of South Carolina数学系，目前于武汉数学与智能研究院从事博士后研究，合作导师为张平文院士。研究方向涵盖最优控制与最优传输、非局部问题的分析、计算与应用，近年在《SIAM J. Appl. Math.》、《SIAM J. Multiscale Model. Simul.》(3篇)、《J. Sci. Comput.》、《Calcolo》等发表20篇文章，主持教育部海外博士后引才专项、中国博士后科学基金面上项目以及省级项目两项。
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