主講人：王曉明 東方理工大學(xué)教授
時(shí)間：2025年10月9日15：00
地點(diǎn)：徐匯校區(qū)三號(hào)樓332室
舉辦單位：數(shù)理學(xué)院
主講人介紹：王曉明教授本科及碩士階段就讀于復(fù)旦大學(xué)數(shù)學(xué)系，后赴美在印第安納大學(xué)伯明頓分校獲得應(yīng)用數(shù)學(xué)博士學(xué)位，并在紐約大學(xué)庫(kù)朗數(shù)學(xué)科學(xué)研究所完成博士后研究。2024年加入東方理工大學(xué)，擔(dān)任數(shù)學(xué)學(xué)科創(chuàng)校講席教授。在此之前，他曾在多所高校擔(dān)任終身教職，包括密蘇里科技大學(xué)首任 Havener 講席系主任、南方科技大學(xué)講席教授、復(fù)旦大學(xué)特聘教授、佛羅里達(dá)州立大學(xué)教授。
王曉明教授長(zhǎng)期致力于現(xiàn)代應(yīng)用數(shù)學(xué)前沿研究，主要方向包括流體動(dòng)力學(xué)、地下水流動(dòng)、地球物理流體力學(xué)、湍流與氣候變化等。他善于融合偏微分方程、動(dòng)力系統(tǒng)、隨機(jī)分析、數(shù)值方法、科學(xué)計(jì)算及機(jī)器學(xué)習(xí)等多種數(shù)學(xué)工具，致力于在嚴(yán)謹(jǐn)數(shù)學(xué)理論與復(fù)雜物理系統(tǒng)之間架起橋梁，推動(dòng)理論突破與交叉創(chuàng)新。他已在《Communications on Pure and Applied Mathematics》（CPAM）等國(guó)際一流期刊發(fā)表學(xué)術(shù)論文一百余篇，并由劍橋大學(xué)出版社出版學(xué)術(shù)專(zhuān)著一本。
內(nèi)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).