A Hele-Shaw type flow with interior and free boundary oscillation
数学专题报告
报告题目(Title)：A Hele-Shaw type flow with interior and free boundary oscillation
报告人(Speaker)：Yuming Paul Zhang (Auburn University)
地点(Place)：Zoom ID: 919 4349 4293, PWD: 354618
时间(Time)：2025 年 3月 14日 9：30-10：30
邀请人(Inviter)：熊金钢
报告摘要
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set. Our contributions are twofold. First, we establish well-posedness and a comparison principle for the problem by introducing a novel notion of viscosity flows. Second, assuming the coefficients are stationary ergodic, we prove a stochastic homogenization result. To derive the effective free boundary velocity, we use a new approximation that accounts for interior homogenization as well as for the free boundary propagation. This is joint work with Olga Turanova.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
