Long-time dynamics for the energy critical heat equation in R5

被引：2
作者：
Li, Zaizheng [1 ]
Wei, Juncheng [2 ]
Zhang, Qidi [3 ]
Zhou, Yifu [4 ]
机构：
[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China
[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[3] Univ Hong Kong, Dept Math, Hong Kong, Peoples R China
[4] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 247卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Energy critical heat equation; Long-time dynamics; Gluing method; HARMONIC MAP FLOW; ASYMPTOTIC-BEHAVIOR; THRESHOLD SOLUTIONS; PARABOLIC EQUATION; GLOBAL-SOLUTIONS; BLOW-UP; DECAY; SINGULARITY; THEOREMS;
D O I：
10.1016/j.na.2024.113594
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the long-time behavior of global solutions to the energy critical heat equation in R-5 {partial derivative(t)u = Delta u + vertical bar u vertical bar(4/3)u in R(5)x(t(0),infinity), u(center dot, t(0)) = u(0) in R-5. For t(0) sufficiently large, we show the existence of positive solutions for a class of initial value u(0)(x) similar to vertical bar x vertical bar(-gamma) as vertical bar x vertical bar -> infinity with gamma > 3/2 such that the global solutions behave asymptotically parallel to u(center dot, t)parallel to(L infinity(R5)) similar to {t(-3(2-gamma)/2) if 3/2 < gamma < 2 (ln t)(-3) if gamma = 2 for t > t(0), 1 if gamma > 2 which is slower than the self-similar time decay t(-3/4). These rates are inspired by Fila and King (2012, Conjecture 1.1).
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页数：15
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