CONVERGENCE TO EQUILIBRIUM FOR SECOND-ORDER DIFFERENTIAL EQUATIONS WITH WEAK DAMPING OF MEMORY TYPE

被引：0

作者：

Zacher, Rico ^{[1
]}

机构：

[1] Univ Halle Wittenberg, Inst Math, D-06120 Halle, Germany

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2009年 / 14卷 / 7-8期

关键词：

DYNAMIC BOUNDARY-CONDITIONS; LONG-TIME BEHAVIOR; VOLTERRA-EQUATIONS; ANALYTIC NONLINEARITY; ASYMPTOTIC-BEHAVIOR; INTEGRAL-EQUATIONS; POSITIVE KERNELS; WAVE-EQUATION; BANACH-SPACES; STEADY-STATES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the asymptotic behavior, as t --> infinity, of hounded solutions to a second-order integro-differential equation in finite dimensions where the damping term is of memory type and can be of arbitrary fractional order less than 1. We derive appropriate Lyapunov functions for this equation and prove that any global bounded solution converges to an equilibrium of a related equation, if the nonlinear potential S occurring in the equation satisfies the Lojasiewicz inequality.

引用

页码：749 / 770

页数：22

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