主講人：王曉明 東方理工大學教授

時間：2025年10月9日15：00

地點：徐匯校區三號樓332室

舉辦單位：數理學院

主講人介紹：王曉明教授本科及碩士階段就讀于復旦大學數學系，后赴美在印第安納大學伯明頓分校獲得應用數學博士學位，并在紐約大學庫朗數學科學研究所完成博士后研究。2024年加入東方理工大學，擔任數學學科創校講席教授。在此之前，他曾在多所高校擔任終身教職，包括密蘇里科技大學首任 Havener 講席系主任、南方科技大學講席教授、復旦大學特聘教授、佛羅里達州立大學教授。

   王曉明教授長期致力于現代應用數學前沿研究，主要方向包括流體動力學、地下水流動、地球物理流體力學、湍流與氣候變化等。他善于融合偏微分方程、動力系統、隨機分析、數值方法、科學計算及機器學習等多種數學工具，致力于在嚴謹數學理論與復雜物理系統之間架起橋梁，推動理論突破與交叉創新。他已在《Communications on Pure and Applied Mathematics》（CPAM）等國際一流期刊發表學術論文一百余篇，并由劍橋大學出版社出版學術專著一本。

內容介紹：Convection in porous media plays a central role in geophysical fluid dynamics, geothermal energy, carbon sequestration, and other climate-related processes. Layered porous structures often arise naturally or through design, leading to systems with abrupt material transitions. In such cases, the Darcy–Boussinesq equations give rise to a nonlinear transmission problem, raising a fundamental question: what interfacial conditions are appropriate?

In this talk, I address this issue by viewing the sharp interface model as the limit of a more physically realistic diffuse-interface formulation, where properties vary smoothly across layers. Assuming constant porosity, we prove that as the transition-layer thickness vanishes, solutions of the diffuse model converge to those of the sharp interface system over finite time intervals for suitable data. The analysis highlights velocity boundary layer formation and requires delicate elliptic and parabolic estimates with nearly discontinuous coefficients. Beyond finite time, we show that both sharp and diffuse models admit global attractors, and these attractors converge as the transition layers shrink.

This work provides a rigorous foundation for the sharp interface approximation, linking it to more realistic diffuse-interface models. I will also discuss implications for long-time dynamics and outline numerical methods adapted to layered porous structures.

This is joint work with Hongjie Dong (Brown University) and Kaijian Sha (EIT).