Global existence of solutions of a semilinear heat equation with nonlinear memory condition

被引：1

作者：

Gladkov, Alexander ^{[1
,2
]}

Guedda, Mohammed ^{[3
]}

机构：

[1] Belarusian State Univ, Dept Math Cybernet, Fac Math & Mech, Minsk, BELARUS

[2] RUDN Univ, Peoples Friendship Univ Russia, Ctr Nonlinear Problems Math Phys, Moscow, Russia

[3] Univ Picardie, CNRS, LAMFA, UMR 6140, Amiens, France

来源：

APPLICABLE ANALYSIS | 2020年 / 99卷 / 16期

关键词：

Alexander Pankov; Semilinear parabolic equation; memory boundary condition; finite time blow-up; BOUNDARY-CONDITION; SOLVABILITY;

D O I：

10.1080/00036811.2019.1584291

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow-up in finite time of all nontrivial solutions. The results depend on the behavior of variable coefficients as t -> infinity .

引用

页码：2823 / 2832

页数：10

共 50 条

[1] Global existence of solutions for the heat equation with a nonlinear boundary condition
Kawakami, Tatsuki
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (01) : 320 - 329
[2] The existence and nonexistence of global solutions for a semilinear heat equation on graphs
Lin, Yong
Wu, Yiting
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (04)
[3] The existence and nonexistence of global solutions for a semilinear heat equation on graphs
Yong Lin
Yiting Wu
[J]. Calculus of Variations and Partial Differential Equations, 2017, 56
[4] GLOBAL EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR SEMILINEAR WAVE EQUATION WITH A NEW CONDITION
Sabitbek, B. O. L. Y. S.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2023, 43 (07) : 2637 - 2657
[5] EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR A DISCRETE SEMILINEAR HEAT EQUATION
Matsuya, Keisuke
Tokihiro, Tetsuji
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 (01) : 209 - 220
[6] Global existence and decay estimates for the semilinear heat equation with memory in Rn
Berbiche, Mohamed
Melik, Ammar
[J]. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (02): : 2271 - 2285
[7] EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR A SEMILINEAR HEAT EQUATION ON A GENERAL DOMAIN
Loayza, Miguel
Da Paixao, Crislene S.
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[8] Global solutions of the heat equation with a nonlinear boundary condition
Kazuhiro Ishige
Tatsuki Kawakami
[J]. Calculus of Variations and Partial Differential Equations, 2010, 39 : 429 - 457
[9] Global solutions of the heat equation with a nonlinear boundary condition
Ishige, Kazuhiro
Kawakami, Tatsuki
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (3-4) : 429 - 457
[10] EXISTENCE OF GLOBAL SOLUTIONS OF SEMILINEAR STOKES EQUATION
丁夏畦
严国政
[J]. Acta Mathematica Scientia, 1993, (02) : 211 - 219

← 1 2 3 4 5 →