SINGULAR LIMIT AND LONG-TIME DYNAMICS OF BRESSE SYSTEMS

被引：59

作者：

Ma, To Fu ^{[1
]}

Monteiro, Rodrigo Nunes ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP, Brazil

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2017年 / 49卷 / 04期

关键词：

Bresse system; Timoshenko system; singular limit; global attractor; exponential attractor; upper-semicontinuity; DECAY-RATE; UPPER SEMICONTINUITY; EQUATION; RATES; DISSIPATION; ATTRACTOR; SPEEDS; ENERGY;

D O I：

10.1137/15M1039894

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Bresse system is a valid model for arched beams which reduces to the classical Timoshenko system when the arch curvature l is zero. Our first result shows the Timoshenko system as a singular limit of the Bresse system as l -> 0. The remaining results are concerned with the long-time dynamics of Bresse systems. In a general framework, allowing nonlinear damping and forcing terms, we prove the existence of a smooth global attractor with finite fractal dimension and exponential attractors as well. We also compare the Bresse system with the Timoshenko system, in the sense of the upper-semicontinuity of their attractors as l -> 0.

引用

页码：2468 / 2495

页数：28

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