Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up

被引：2

作者：

Shi, Jincheng ^{[1
]}

Zhang, Yan ^{[2
]}

Cai, Zihan ^{[3
]}

Liu, Yan ^{[3
]}

机构：

[1] Guangzhou Huashang Coll, Coll Data Sci, Huashang Rd, Guangzhou 511300, Peoples R China

[2] Guangdong Teachers Coll Foreign Language & Arts, Dept Appl Math, Longdong East Rd, Guangzhou 510521, Peoples R China

[3] Guangdong Univ Finance, Dept Appl Math, Yingfu Rd, Guangzhou 510521, Peoples R China

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Moore-Gibson-Thompson equation; derivative-type nonlinearity; global existence of small data solution; decay estimate; blow-up; WAVE-EQUATION;

D O I：

10.3934/math.2022015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type jutjp. We demonstrate global existence of small data solutions if p > 1 + 4/n (n <= 6) or p >= 2 - 2/n (n >= 7), and blow-up of nontrivial weak solutions if 1 < p <= 1 + 1/n. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by [4].

引用

页码：247 / 257

页数：11

共 50 条

[41] Well-posedness for a fourth-order equation of Moore-Gibson-Thompson type
Lizama, Carlos
Murillo, Marina
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2021, (81) : 1 - 18
[42] Global Existence and Blow-Up for a Parabolic Problem of Kirchhoff Type with Logarithmic Nonlinearity
Hang Ding
Jun Zhou
Applied Mathematics & Optimization, 2021, 83 : 1651 - 1707
[43] Global Existence and Blow-Up for a Parabolic Problem of Kirchhoff Type with Logarithmic Nonlinearity
Ding, Hang
Zhou, Jun
APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 83 (03): : 1651 - 1707
[44] Global existence and blow-up of solutions for a semilinear parabolic system
Chen, SH
Derrick, WR
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (02) : 449 - 457
[45] SOLVABILITY OF THE MOORE-GIBSON-THOMPSON EQUATION WITH VISCOELASTIC MEMORY TYPE II AND INTEGRAL CONDITION
Boulaaras, Salah
Choucha, Abdelbaki
Ouchenane, Djamel
Abdalla, Mohamed
Vazquez, Aldo Jonathan Munoz
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (06): : 1216 - 1241
[46] Blow-up at infinity of solutions to a semilinear heat equation with logarithmic nonlinearity
Han, Yuzhu
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) : 513 - 517
[47] Global existence for the Jordan-Moore-Gibson-Thompson equation in Besov spaces
Said-Houari, Belkacem
JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (02)
[48] Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms
Zhang, Hongwei
Zhang, Wenxiu
Hu, Qingying
BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)
[49] Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms
Hongwei Zhang
Wenxiu Zhang
Qingying Hu
Boundary Value Problems, 2019
[50] Existence and blow-up of solutions in Henon-type heat equation with exponential nonlinearity
Gao, Dongmei
Wang, Jun
Wang, Xuan
ADVANCES IN NONLINEAR ANALYSIS, 2023, 12 (01)

← 1 2 3 4 5 →