Stability Results for a Timoshenko System with a Fractional Operator in the Memory

被引：10
作者：
Astudillo, Maria [1 ]
Oquendo, Higidio Portillo [1 ]
机构：
[1] Univ Fed Parana, Math Postgrad Program, Curitiba, Parana, Brazil
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 83卷 / 03期
关键词：
Timoshenko system; Fractional damping; Memory term; Exponential stability; Polynomial decay; ENERGY DECAY; STABILIZATION; FOURIER; RATES;
D O I：
10.1007/s00245-019-09587-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the asymptotic behavior of Timoshenko systems with a fractional operator in the memory term depending on a parameter.. [0, 1] and acting only on one equation of the system. Considering exponentially decreasing kernels, we find exact decay rates. To be precise, we show that for.. [0, 1), the system decay polynomially with rates that depend on the value of the difference of the wave propagation speeds. We also prove that these decay rates are optimal. Moreover, when. = 1 and the equations have the same propagation speeds we obtain the exponential decay of the solutions.
引用
收藏
页码：1247 / 1275
页数：29
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