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

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