Global existence of solutions and energy decay for a Kirchhoff-type equation with nonlinear dissipation

被引：3

作者：

Ye, Yaojun ^{[1
]}

机构：

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

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年

关键词：

nonlinear Kirchhoff-type equation; initial boundary value problem; stable set; energy decay estimate; HYPERBOLIC-EQUATIONS; LOCAL SOLUTIONS; WAVE-EQUATIONS;

D O I：

10.1186/1029-242X-2013-195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equation with dissipative term u(tt) - phi(parallel to del u parallel to(2)(2))Delta u + a vertical bar u(t)vertical bar(alpha-2)u(t) = b vertical bar u vertical bar(beta-2)u, x is an element of Omega, t > 0 in a bounded domain, where a, b > 0 and alpha, beta > 2 are constants. We obtain the global existence of solutions by constructing a stable set in H-0(1)(Omega) and show the energy decay estimate by applying a lemma of Komornik.

引用

页数：10

共 50 条

[1] Global existence of solutions and energy decay for a Kirchhoff-type equation with nonlinear dissipation
Yaojun Ye
Journal of Inequalities and Applications, 2013 (1)
[2] Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation
Kim, Daewook
Kim, Dojin
Hong, Keum-Shik
Jung, Il Hyo
SCIENTIFIC WORLD JOURNAL, 2014,
[3] Global existence and energy decay estimate of solutions for a higher-order Kirchhoff type equation with damping and source term
Ye, Yaojun
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (06) : 2059 - 2067
[4] Existence and blow-up of solutions for higher-order Kirchhoff-type equation
Ye, Yaojun
Chang, Shuting
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2025, 74 (02)
[5] GLOBAL SOLUTIONS FOR A NONLINEAR KIRCHHOFF TYPE EQUATION WITH VISCOSITY
Lapa, Eugenio Cabanillas
OPUSCULA MATHEMATICA, 2023, 43 (05) : 689 - 701
[6] LOCAL EXISTENCE AND BLOW UP OF SOLUTIONS FOR A COUPLED VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH DEGENERATE DAMPING
Piskin, Erhan
Ekinci, Fatma
MISKOLC MATHEMATICAL NOTES, 2021, 22 (02) : 861 - 874
[7] Global existence and asymptotic behavior of solutions for a system of higher-order Kirchhoff-type equations
Ye, Yaojun
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2015, (20) : 1 - 12
[8] Global existence and energy decay for a coupled system of Kirchhoff type equations with damping and source terms
Ye, Yao-jun
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2016, 32 (03): : 731 - 738
[9] Global attractor for the Kirchhoff type equation with a strong dissipation
Yang Zhijian
Wang Yunqing
JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (12) : 3258 - 3278
[10] Coupled system of nonlinear viscoelastic plate equations of (p(x), q(x))-Kirchhoff-type: Global existence, general decay, and blow-up
Shahrouzi, Mohammad
Ferreira, Jorge
Tahamtani, Faramarz
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (04) : 2472 - 2499

← 1 2 3 4 5 →