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 DECAY ESTIMATES FOR NONLINEAR KIRCHHOFF-TYPE EQUATION WITH BOUNDARY DISSIPATION
Lin, Xiuli
Li, Fushan
DIFFERENTIAL EQUATIONS & APPLICATIONS, 2013, 5 (02): : 297 - 317
[4] Global existence and blow-up of solutions for a higher-order Kirchhoff-type equation with nonlinear dissipation
Li, FC
APPLIED MATHEMATICS LETTERS, 2004, 17 (12) : 1409 - 1414
[5] Global existence and energy decay of solutions for Kirchhoff-Carrier equations with weakly nonlinear dissipation
Benaissa, A
Rahmani, L
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2004, 11 (04) : 547 - 574
[6] Energy decay of solutions of a degenerate Kirchhoff equation with a weak nonlinear dissipation
Abdelli, Mama
Benaissa, Abbes
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (07) : 1999 - 2008
[7] Existence and Multiplicity of Solutions for Fractional κ(ξ)-Kirchhoff-Type Equation
Sousa, J. Vanterler da C.
Kucche, Kishor D.
Nieto, Juan J.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (01)
[8] Existence of solutions for a p(x)-Kirchhoff-type equation
Dai, Guowei
Hao, Ruifang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) : 275 - 284
[9] Global existence and energy decay of small solutions to the Kirchhoff equation with linear dissipation localized near infinity
Mochizuki, K
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1999, 39 (02): : 347 - 363
[10] On the existence of least energy solutions to a Kirchhoff-type equation in R3
Lu, Dengfeng
Lu, Zongze
APPLIED MATHEMATICS LETTERS, 2019, 96 : 179 - 186

← 1 2 3 4 5 →