Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions

被引：2

作者：

Zhang, Jian ^{[1
]}

Radulescu, Vicentiu D. ^{[1
,2
,3
,4
]}

Yang, Minbo ^{[1
]}

Zhou, Jiazheng ^{[5
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

[3] Univ Craiova, Dept Math, Craiova 200585, Romania

[4] Brno Univ Technol, Fac Elect Engn & Commun, Tech 3058-10, Brno 61600, Czech Republic

[5] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2025年 / 37卷 / 01期

关键词：

Nonlocal parabolic equation; Hardy-Littlewood-Sobolev critical exponent; Global existence; Asymptotic behavior; Finite time blow-up; NONEXISTENCE THEOREMS; HEAT-EQUATION; WAVE-FRONTS; INSTABILITY;

D O I：

10.1007/s10884-023-10278-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy-Littlewood-Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for J(mu)(u0) < 0 and decay rate of H-0(1) and L-2-norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation.

引用

页码：687 / 725

页数：39

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