报告人简介

张俊华，博士毕业于北京师范大学，师从李海刚教授。现任职南昌大学师资博士后。主要从事非线性分和和椭圆型方程的研究工作，在 Calc. Var. Partial Differential Equations, SIAM Journal on Applied Mathematics等国际知名期刊发表论文多篇。

报告内容简介

The Babuška problem, originating from the seminal work of Ivo Babuška on high-contrast composite materials, concerns the mathematical analysis of stress concentration and field enhancement in the presence of inclusions with extreme parameter contrasts. This framework provides a rigorous foundation for understanding critical phenomena such as gradient blow-up, anomalous resonance, and subwavelength resonance in structured media. In this talk, we will present recent advances on the Babuška problem and demonstrate how our analytical results can be applied to subwavelength resonance systems in both acoustic and elastic regimes.

巴布斯卡问题源于伊沃·巴布斯卡关于高对比度复合材料的开创性研究，主要涉及在存在具有极端参数差异的夹杂物时，应力集中与场增强现象的数学分析。该理论框架为理解结构化介质中的梯度爆增、异常共振及亚波长共振等关键现象提供了严谨的基础。在本次报告中，我们将介绍巴布斯卡问题领域的最新研究成果，并演示如何将我们的分析结果应用于声学与弹性体系中的亚波长共振系统。