Speaker: 李海刚教授，北京师范大学

Inviter: 流体力学方程研究中心

Title: Babuska Problem and its Applications in Subwavelength Resonance and Fluid-Solid Suspension Problem

Language: Chinese 

Time & Venue: 2025.04.24  10:30-11:30  南楼N202

Abstract: In high-contrast composite materials, stress concentration occurs in the narrow regions between adjacent hard inclusions as they approach close proximity. Significant progress has been made over the past two decades in understanding such concentration phenomenon. In this talk we will show two related problems. In this talk, we address two interrelated problems:

1.Resonant Behavior in Acoustic Systems: We demonstrate how gradient estimates derived for the electrostatic equation can be extended to analyze resonant interactions in systems of closely spaced acoustic subwavelength resonators.

2.Stress Concentration in Fluid-Solid Systems: We show that the energy iteration method, originally developed to solve the Babuska problem, can be generalized to study stress concentration between two adjacent convex rigid particles suspended in stationary Stokes/Navier-Stokes flows.

Recently, the singularities of higher-order derivatives of solutions for the Lam\'e system and the Stokes equations in between closely spaced inclusions are both derived.