Gluing method and blow-up solutions for the energy critical nonlinear heat equation

发布时间：2018-06-21 作者：浏览次数：

Speaker:	郑有泉副教授	DateTime:	2018年6月25日（周一）上午9:00-10:00
Brief Introduction to Speaker: 郑有泉,天津大学数学学院副教授。		Place:	六号楼二楼报告厅
Abstract:Considering positive solutions for the fractional heat equation with critical exponent on a smooth bounded domain $\Omega$, we prove the existence of initial datum such that the solution blows up precisely at prescribed distinct points $q_1,\cdots, q_k$ in $\Omega$ as $t\to +\infty$. The main ingredient of the proofs is a new inner-outer gluing scheme for the fractional parabolic problems. We also apply this method in the construction of sign-changing blow-up solutions for the energy critical nonlinear heat equation in large dimensions. These are joint works with Professor Juncheng Wei.