论文标题
非平滑直接/间接弹性/粘弹性阻尼问题的多项式稳定涉及BRESSE系统
Polynomial stabilization of non-smooth direct/indirect elastic/viscoelastic damping problem involving Bresse system
论文作者
论文摘要
我们考虑了带有Dirichlet或Dirichlet-Neumann-Neumann边界条件的Bresse系统的弹性/粘弹性传输问题。物理模型由以某些模式结合的三个波方程组成。该系统由全球或局部开尔文 - voigt阻尼直接或间接阻尼。实际上，在接口的稳定类型中，阻尼的数量，它们的分布性质（局部或全球）的性质（局部或全球）以及阻尼系数的平滑度在相应的半群的稳定类型中起着至关重要的作用。实际上，使用频域方法与乘数技术结合并构建新的乘数函数，我们建立了不同类型的能量衰减速率（请参阅下面的稳定表结果）。我们的结果在文献中概括并改善了许多早期的研究，尤其是一些对Timoshenko系统进行的研究。
We consider an elastic/viscoelastic transmission problem for the Bresse system with fully Dirichlet or Dirichlet-Neumann-Neumann boundary conditions. The physical model consists of three wave equations coupled in certain pattern. The system is damped directly or indirectly by global or local Kelvin-Voigt damping. Actually, the number of the dampings, their nature of distribution (locally or globally) and the smoothness of the damping coefficient at the interface play a crucial role in the type of the stabilization of the corresponding semigroup. Indeed, using frequency domain approach combined with multiplier techniques and the construction of a new multiplier function, we establish different types of energy decay rate (see the table of stability results below). Our results generalize and improve many earlier ones in the literature and in particular some studies done on the Timoshenko system with Kelvin-Voigt damping.
