论文标题
具有粘弹性无限记忆的多维非线性压电束的稳定性
Stability of Multi-dimensional Nonlinear Piezoelectric Beam with Viscoelastic Infinite Memory
论文作者
论文摘要
考虑了具有粘弹性无限记忆的一种完全磁性的非线性压电束的长时间行为。该非线性耦合PDES系统的适应性通过半群理论和Banach固定点定理显示。基于频域分析，证明只能通过一个粘弹性的无限内存项，可以间接地稳定相应的线性系统，该系统位于这些强耦合PDES的一个方程式上。然后，在某些条件下的能量估计方法建立了解决方案对非线性耦合PDES系统的指数衰减。
The long time behavior of a kind of fully magnetic effected nonlinear piezoelectric beam with viscoelastic infinite memory is considered. The well-posedness of this nonlinear coupled PDEs system is showed by mean of the semigroup theories and Banach fixed point theorem. Based on frequency domain analysis, it is proved that the corresponding coupled linear system can be indirectly stabilized exponentially by only one viscoelastic infinite memory term, which is located on one equation of these strongly coupled PDEs. Then the exponential decay of the solution to the nonlinear coupled PDEs' system is established by the energy estimation method under certain condition.
