Global Existence and Blow-up of Solutions for a Class of Singular Parabolic Equations with Viscoelastic Term

被引：1

作者：

Gao, Yanchao ^{[1
]}

Jia, Wenxu ^{[1
]}

Feng, Zhixin ^{[2
]}

机构：

[1] Changchun Univ Sci & Technol, Sch Math & Stat, Changchun 130022, Peoples R China

[2] Jilin Normal Univ, Sch Math & Comp, Siping 136000, Peoples R China

来源：

JOURNAL OF FUNCTION SPACES | 2024年 / 2024卷

关键词：

SEMILINEAR HEAT-EQUATION;

D O I：

10.1155/2024/5754129

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the initial boundary value problem for a class of singular parabolic equations with viscoelastic term and logarithmic term. By using the technique of cut-off and the method of Faedo-Galerkin approximation, the local existence of the weak solution is established. Based on the potential well method, the global existence of the weak solution is derived. Furthermore, we prove that the weak solution blows up in finite time by taking the concavity analysis method.

引用

页数：12

共 50 条

[31] Global Existence and Blow-Up in a p(x)-Laplace Equation with Dirichlet Boundary Conditions [J].

Jian, Yuhua ;

Yang, Zuodong .

JOURNAL OF MATHEMATICAL STUDY, 2019, 52 (02) :111-126

[32] The blow-up properties of solutions to semilinear heat equations with Neumann boundary conditions [J].

Lin, ZG .

ACTA MATHEMATICA SCIENTIA, 1998, 18 (03) :315-325

[33] Existence of solutions semilinear parabolic equations with singular initial data in the Heisenberg group [J].

Bui, The Anh ;

Hisa, Kotaro .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2024,

[34] Blow-up for a semilinear parabolic equation with large diffusion on RN [J].

Fujishima, Yohei ;

Ishige, Kazuhiro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (05) :2508-2543

[35] Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity [J].

Filippas, S ;

Herrero, MA ;

Velázquez, JJL .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2000, 456 (2004) :2957-2982

[36] Numerical finite difference approximations of a coupled parabolic system with blow-up [J].

Khalil, Manar I. ;

Hashim, Ishak ;

Rasheed, Maan A. ;

Ismail, Eddie S. .

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2024, 32 (04) :387-407

[37] Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity [J].

Yan, Lijun ;

Yang, Zuodong .

BOUNDARY VALUE PROBLEMS, 2018,

[38] Blow-up for a semilinear parabolic equation with large diffusion on RN. II [J].

Fujishima, Yohei ;

Ishige, Kazuhiro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (02) :1835-1861

[39] ON INSTANT BLOW-UP FOR SEMILINEAR HEAT EQUATIONS WITH GROWING INITIAL DATA [J].

Giga, Yoshikazu ;

Umeda, Noriaki .

METHODS AND APPLICATIONS OF ANALYSIS, 2008, 15 (02) :185-195

[40] On blow-up rate for sign-changing solutions in a convex domain [J].

Giga, Y ;

Matsui, S ;

Sasayama, S .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2004, 27 (15) :1771-1782

← 1 2 3 4 5 →