勷勤数学•专家报告

题      目：Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions

报  告  人：曾小雨 教授  (邀请人：钟学秀)

                                             武汉理工大学

时      间： 8月21日  09：30-10:30

地     点：数科院西楼二楼会议室

报告人简介:

          曾小雨，博士生导师，武汉理工大学数学科学研究中心教授。国家自然科学基金优秀青年科学基金获得者（2023年）、湖北省“青年拔尖人才”入选者（2022年）。主要研究方向为非线性泛函分析及椭圆型偏微分方程，聚焦于薛定谔方程、玻色-爱因斯坦凝聚中的变分问题，在质量临界约束变分理论、量子多体系统分析等领域取得系统性突破。主持国家自然科学基金项目4项（含优青、面上、青年项目），参与国家自然科学基金重点项目2项。在Trans. Amer. Math. Soc. (TAMS)、J. Funct. Anal. (JFA)、Ann. Inst. H. Poincaré Anal. Non Linéaire、Nonlinearity、J. Differential Equations (JDE)等国际知名期刊发表论文50余篇，研究成果被国际同行广泛引用并引发后续研究

摘      要：

        In this talk, we consider a five-dimensional heat equation with critical boundary conditions. Given distinct finitely many boundary points $q^{[i]} \in \partial \mathbb{R}_+^5$, and integers $l_i$ (possibly repeated), we construct, for $T>0$ sufficiently small, a finite-time blow-up solution $u$ with a type II blow-up rate $(T-t)^{-3l_i -3}$ for $x$ near $q^{[i]}$. To accommodate highly unstable blowups with different blowup rates, we first develop a unified linear theory for the inner problem with more time decay in the blow-up scheme through restriction on the spatial growth of the right-hand side, and then use vanishing adjustment functions for deriving multiple rates at distinct points. This is joint work with Juncheng Wei, Zikai Ye, and Qidi Zhang.

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