Mathematical effects of linear visco-elasticity in quasi-static Biot models
Mathematical effects of linear visco-elasticity in quasi-static Biot models
复制标题
准静态 Biot 模型中线性粘弹性的数学效应
DOI：
10.1016/j.jmaa.2023.127462
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发表时间：
2023
影响因子：
1.3
通讯作者：
Webster, Justin T.
中科院分区：
文献类型：
--
作者：
Bociu, Lorena;Muha, Boris;Webster, Justin T.
我们调查和澄清的数学性质的线性多孔弹性系统中存在的经典（线性，Kelvin-Voigt）粘弹性。特别是，我们量化的时间正则化和耗散效应的粘弹性的准静态毕奥方程的上下文中。充分，耦合的压力-位移介绍的系统，以及隐式，退化的演化方程的框架，以证明这样的效果和特征linearporo粘弹性系统。我们考虑一个简单的动态演示（方便的边界条件等）。为了在几个相关参数范围内清楚地说明。提供了明确的适定性结果，与相关的先验估计的解决方案。此外，在每种情况下，允许的初始条件的精确陈述。
We investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of visco-elasticity in the context of the quasi-static Biot equations. The full, coupled pressure-displacement presentation of the system is utilized, as well as the framework of implicit, degenerate evolution equations, to demonstrate such effects and characterize linearporo-visco-elastic systems. We consider a simple presentation of the dynamics (with convenient boundary conditions, etc.) for clarity in exposition across several relevant parameter ranges. Clear well-posedness results are provided, with associated a priori estimates on the solutions. In addition, precise statements of admissible initial conditions in each scenario are given.