We consider a swelling porous-elastic system with a single nonlinear damping in the elastic equation. Recently, Ramos et al. [Stability results for elastic porous media swelling with nonlinear damping. J Math Phys. 2020;61(10):101505.] considered the same system and established a general decay result provided that the wave speeds of the system are equal. In this paper, we obtain the general decay result without imposing a condition on the wave speeds of the system. This is a striking and unexpected result compared to Timoshenko system, porous systems, and Laminated beams system with similar damping. We also perform some numerical tests to illustrate our theoretical results.

我们考虑在弹性方程中具有单一非线性阻尼的膨胀多孔弹性系统。最近，拉莫斯等人。[具有非线性阻尼的弹性多孔介质膨胀的稳定性结果。J 数学物理学。2020;61(10):101505.] 考虑相同的系统并建立一般衰减结果，前提是系统的波速相等。在本文中，我们在不对系统的波速施加条件的情况下获得了一般衰减结果。与 Timoshenko 系统、多孔系统和具有类似阻尼的层压梁系统相比，这是一个惊人且出乎意料的结果。我们还进行了一些数值测试来说明我们的理论结果。