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).

引用

页数：15

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