Existence and blow-up of solutions for higher-order Kirchhoff-type equation

被引：0

作者：

Ye, Yaojun ^{[1
]}

Chang, Shuting ^{[1
]}

机构：

[1] Zhejiang Univ Sci & Technol, Dept Math & Stat, Hangzhou 310023, Peoples R China

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2025年 / 74卷 / 02期

关键词：

Higher-order Kirchhoff-type equation; Initial-boundary value problem; Local and global solutions; Blow up; Lifespan of solution; GLOBAL EXISTENCE; ASYMPTOTIC STABILITY; WAVE-EQUATIONS; ENERGY DECAY; SYSTEM;

D O I：

10.1007/s12215-025-01201-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the initial-boundary value problem for a model equation of higher-order Kirchhoff-type in a bounded domain. The existence of local and global solutions for this problem are proved by means of the contraction mapping criterion and potential well method. Meanwhile, we obtain the blow-up result of solution in the unstable set by using the concavity analysis method and give the lifespan estimate of solution.

引用

页数：13

共 35 条

[1] Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations
Aliev, Akbar B.
Lichaei, Bijan H.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (7-8) : 3275 - 3288
[2] Arora R., 2023, Adv. Nonlinear Anal, V12, P1
[3] Existence and multiplicity of solutions for a new p(x)-Kirchhoff equation
Chu, Changmu
Liu, Jiaquan
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2024, 13 (01)
[4] Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point
Diblik, Josef
Ruzickova, Miroslava
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2024, 13 (01)
[5] Blow-up and critical exponents for nonlinear hyperbolic equations
Galaktionov, VA
Pohozaev, SI
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 53 (3-4) : 453 - 466
[6] Existence and classification of positive solutions for coupled purely critical Kirchhoff system
Gao, Yahui
Luo, Xiao
Zhen, Maoding
[J]. BULLETIN OF MATHEMATICAL SCIENCES, 2024, 14 (02)
[7] Global solutions and finite time blow up for damped semilinear wave equations
Gazzola, F
Squassina, M
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (02): : 185 - 207
[8] Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions
Gerbi, S.
Said-Houari, B.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) : 7137 - 7150
[9] Gerbi S., 2008, Adv. Differential Equations, V13, P1051
[10] EXPONENTIAL DECAY FOR SOLUTIONS TO SEMILINEAR DAMPED WAVE EQUATION
Gerbi, Stephane
Said-Houari, Belkacem
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2012, 5 (03): : 559 - 566

← 1 2 3 4 →