Blow-up of solutions to a viscoelastic parabolic equation with positive initial energy

被引：0

作者：

Li, Haixia ^{[1
]}

Han, Yuzhu ^{[2
]}

机构：

[1] Changchun Normal Univ, Sch Math, Changchun 130032, Peoples R China

[2] Jilin Univ, Sch Math, 2699 Qianjin St, Changchun 130012, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2017年

关键词：

viscoelastic; potential well method; blow-up; nonlinear boundary flux; SEMILINEAR HEAT-EQUATION;

D O I：

10.1186/s13661-017-0821-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a semilinear viscoelastic parabolic equation with nonlinear boundary flux is studied. Due to the comparison principle being invalid, potential well method and concavity argument are used to prove that the solutions blow up in finite time with positive initial energy. This result improves the one obtained by Han et al. (C. R. Math. Acad. Sci. Paris, Ser. I 353:825-830, 2015).

引用

页数：9

共 50 条

[1] Blow-up of solutions to a viscoelastic parabolic equation with positive initial energy
Haixia Li
Yuzhu Han
[J]. Boundary Value Problems, 2017
[2] A note on blow-up of solutions for the nonlocal quasilinear parabolic equation with positive initial energy
Fang, Zhong Bo
Sun, Lu
Li, Changjun
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[3] Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation
Messaoudi, Salim A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (02) : 902 - 915
[4] A note on blow-up of solutions for the nonlocal quasilinear parabolic equation with positive initial energy
Zhong Bo Fang
Lu Sun
Changjun Li
[J]. Boundary Value Problems, 2013
[5] Blow-up of a nonlocal semilinear parabolic equation with positive initial energy
Gao, Wenjie
Han, Yuzhu
[J]. APPLIED MATHEMATICS LETTERS, 2011, 24 (05) : 784 - 788
[6] Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy
Wu, Xiulan
Guo, Bin
Gao, Wenjie
[J]. APPLIED MATHEMATICS LETTERS, 2013, 26 (05) : 539 - 543
[7] On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy
Wang, Hua
He, Yijun
[J]. APPLIED MATHEMATICS LETTERS, 2013, 26 (10) : 1008 - 1012
[8] On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy
Li, Gang
Sun, Yun
Liu, Wenjun
[J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
[9] Blow-up phenomena for a nonlocal semilinear parabolic equation with positive initial energy
Khelghati, Ali
Baghaei, Khadijeh
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (05) : 896 - 902
[10] Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation
Song, Haitao
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 26 : 306 - 314

← 1 2 3 4 5 →