In the current study, we analyze the asymptotic behavior of the solutions of one-dimensional initial boundary value problem associated with the isothermal linear theory of swelling porous elastic media. Our main results are the well-posedness of the system as well as the exponential stabilization of solution and the discretization of the equations using a particular numerical scheme, which allowed us to prove the monotonicity of the discrete energy. In addition, we provide the numerical simulations of the solution and the total energy that explain the results obtained. Our results are achieved by using the semigroup theory and for the results in finite dimensional we used finite differences.

中文翻译：

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流体饱和膨胀多孔弹性土的稳定与数值处理

在当前的研究中，我们分析了与膨胀多孔弹性介质的等温线性理论相关的一维初始边值问题解的渐近行为。我们的主要结果是系统的适定性以及解的指数稳定性和使用特定数值方案的方程的离散化，这使我们能够证明离散能量的单调性。此外，我们提供了解的数值模拟和解释所得结果的总能量。我们的结果是通过使用半群理论获得的，对于有限维的结果，我们使用了有限差分。