Nonexistence of Type II Blowup for an Energy-Critical Heat Equation -

Nonexistence of Type II Blowup for an Energy-Critical Heat Equation

发布时间：2022年06月20日浏览次数：3013 发布者: Wenqiong Li

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主讲人： 魏军城（英属哥伦比亚大学）

活动时间： 从 2022-06-21 11:00 到 12:00

场地： 线上

Abstract:
In this talk we prove that all blow-ups for the following energy critical heat equation
$$ u_t=\Delta u + u^{(n+2)/(n-2)}, u(x,0)= u_0 \geq 0 $$

are of Type I, provided that $n\geq 7$. No radial symmetry or finite energy condition is assumed. The proof is built on several key ingredients: first we perform tangent flow analysis and study bubbling formation in this process; next we give a second order bubbling analysis in the multiplicity one case, where we use a reverse inner-outer gluing mechanism; finally, in the higher multiplicity case (bubbling tower/cluster), we develop Schoen's Harnack inequality and obtain next order estimates in Pohozaev identities for critical parabolic flows. (Joint work with Kelei Wang.)

Speaker:

Prof. Juncheng Wei is currently a Professor of Mathematics and a Canada Research Chair (Tier I) at the University of British Columbia, Canada. He works in the area of nonlinear partial differential equations, nonlinear analysis and mathematical biology. He received a Silver Morningside Medal in 2010, and was an invited speaker at the 2014 International Congress of Mathematicians. He was elected a Fellow of the Royal Society of Canada FRSC in 2019, and he was awarded in 2020 the CMS Jeffery-Williams Prize and Simons Fellow in Mathematics. Since 1994, Prof. Wei has over 470 published articles in top journals, including Annals of Mathematics, Inventiones Mathematicae, Communications on Pure and Applied Mathematics, and Duke Mathematical Journal.

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