中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：王克磊（武汉大学）
题 目：Stable and finite Morse index solutions of Allen-Cahn equation
时 间：2023.06.13（星期二）15:00-16:00
地 点：腾讯会议：783-249-741
摘 要：The stability condition and finite Morse index condition play an important role in the classification of solutions to Allen-Cahn equation. Therefore, understanding stable and finite Morse index solutions is always a central topic in the study of Allen-Cahn equation. In this talk I will first briefly review some problems in this direction such as De Giorgi conjecture and stable De Giorgi conjecture. Then I will discuss some results on stable and finite Morse index solutions of Allen-Cahn equation, as well as some tools used in the proof of these results, in particular, the reverse Lyapunov-Schmidt reduction method.
个人简介：王克磊，现为武汉大学数学与统计学院教授。他2010年于中科院数学所获博士学位，曾在悉尼大学从事博士后研究及（原）中科院武汉物理与数学研究所工作。他的研究兴趣主要在于椭圆与抛物型偏微分方程的几何与定性性质方面，尤其是与几何测度论问题相关的奇性分析问题，例如相位分离模型及其极限自由边界问题、非线性椭圆方程的稳定解与有限Morse指标解、Allen-Cahn方程的De Giorgi猜想及有限Morse指标解的分类问题等。
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