Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-05-03 , DOI: 10.1016/j.jde.2021.04.028 M.M. Cavalcanti , V.N. Domingos Cavalcanti , M.A. Jorge Silva , V. Narciso
In this paper, motivated by recent papers on the stabilization of evolution problems with nonlocal degenerate damping terms, we address an extensible beam model with degenerate nonlocal damping of Balakrishnan-Taylor type. We discuss initially on the well-posedness with respect to weak and regular solutions. Then we show for the first time how hard is to guarantee the stability of the energy solution (related to regular solutions) in the scenarios of constant and non-constant coefficient of extensibility. The degeneracy (in time) of the single nonlocal damping coefficient and the methodology employed in the stability approach are the main novelty for this kind of beam models with degenerate damping.
中文翻译:
具有Balakrishnan-Taylor类型的单个简并非局部阻尼的可伸缩梁的稳定性
在本文中,受有关具有非局部简并阻尼项的演化问题的稳定化的最新论文的启发,我们提出了具有Balakrishnan-Taylor型退化非局部阻尼的可扩展梁模型。我们首先讨论关于弱和常规解决方案的适当条件。然后,我们首次展示了在恒定和非恒定可扩展系数的情况下,如何保证能量解决方案(与常规解决方案有关)的稳定性有多么困难。单一非局部阻尼系数的退化(及时性)和在稳定性方法中采用的方法是这种具有退化阻尼的梁模型的主要新颖之处。