ASYMPTOTIC PROPERTIES FOR A SEMILINEAR PLATE EQUATION IN UNBOUNDED DOMAINS

被引：52

作者：

Da Luz, Cleverson Roberto ^{[1
]}

Charao, Ruy Coimbra ^{[2
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Math, BR-21945970 Rio De Janeiro, Brazil

[2] Univ Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC, Brazil

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2009年 / 6卷 / 02期

关键词：

Plate equation; uniform decay rates; unbounded domains; WAVE-EQUATION; EXTERIOR DOMAINS; ENERGY DECAY; GLOBAL EXISTENCE; SYSTEM;

D O I：

10.1142/S0219891609001824

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence, uniqueness, and asymptotic properties of global solutions to the initial value problem associated with a semilinear, dissipative, plate equation under rotational inertia effects in R-n. We obtain polynomial decay rate in time for the total energy. In dimension n >= 5 for the linear problem and n = 5 for the semilinear problem with small data, we obtain fast decay of the total energy and a decay rate t(-1/2) for L-2-norm of the solution and similar decay rates for the L-2-norm of higher-order derivatives.

引用

页码：269 / 294

页数：26

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