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数学学科现代分析及其应用研究所（2021非线性分析与偏微分方程系列报告会五十七）

 2021非线性分析与偏微分方程学术报告报告题目1：Blow up solutions for energy critical heat equation and harmonic map flow报告人：郑有泉（天津大学）报告时间：10月20日（周三），14：00-15：00腾讯会议ID: 870 933 314https://meeting.tencent.com/dm/DEFtiAzQC2RX 摘要：  I will discuss the parabolic gluing method and its applications on constructing blow up solutions for energy critical heat equation,nonlocal harmonic map flow as well as harmonic map flow with free boundary. 报告人简介：郑有泉，天津大学副教授，2011年博士毕业于南开大学；主要研究领域为非线性偏微分方程及其应用，担任国家青年基金项目，教育部博士点基金项目主持人；主要研究结果发表在JDE、JFA、CVPDE等国际学术期刊上。 报告题目2：Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical报告人：钟学秀（华南师范大学）会议时间：10月20日（周三）15：00-16：00腾讯会议ID：870 933 314https://meeting.tencent.com/dm/DEFtiAzQC2RX 摘要：In present paper, we study the normalized solutions $(\lambda_c, u_c)\in \R\times H^1(\R^N)$ to the following Kirchhoff problem$$-\left(a+b\int_{\R^N}|\nabla u|^2dx\right)\Delta u+\lambda u=g(u)~\hbox{in}~\R^N,\;1\leq N\leq 3$$satisfying the normalization constraint$\displaystyle\int_{\R^N}u^2=c,$which appears in free vibrations of elastic strings.  The parameters $a,b>0$ are prescribed as is the mass $c>0$. The nonlinearities $g(s)$ considered here are very general and of mass super-critical. Under some suitable assumptions, we can prove the existence of  ground state normalized solutions for any given $c>0$. After a detailed analysis via the blow up method, we also make clear the asymptotic behavior of these solutions as $c\rightarrow 0^+$ as well as $c\rightarrow+\infty$. 报告人简介：钟学秀，华南师范大学副研究员，2015年博士毕业于清华大学。主要研究领域为非线性偏微分方程及其应用，主要研究成果发表在Math. Ann., JDG, CVPDE，CCM.等国际学术期刊上。邀请人：非线性分析与PDE团队