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Gluing method and blow-up solutions for the energy critical nonlinear heat equation
郑有泉 副教授(天津大学)
2018-06-28 13:33  闵行数学楼402报告厅

摘要: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.

报告人简介:郑有泉,2011年博士毕业于南开大学,现为天津大学数学学院副教授;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。

邀请人:王丽萍