论文标题
非线性准静态孔隙弹性
Nonlinear Quasi-static Poroelasticity
论文作者
论文摘要
我们分析了可压缩和不可压缩成分的毛弹性的准静态生物系统。该模型的主要特征是通过系统的渗透率张量将压力和扩张的非线性耦合。从完全离散的方法构建弱解决方案的角度，先前已经对这种模型进行了分析。在这种处理中，我们考虑了弹性位移和压力变量中的简化Dirichlet类型边界条件，并给出了弱溶液的全面处理。我们针对非线性问题的弱解决方案的构建是基于先验估计值，这是解决非线性的必要特征。我们利用空间半差异化，并采用多价值的固定点论证来清晰地结构弱解决方案。我们还提供有关解决方案独特性的规律性标准。
We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a model has been analyzed previously from the point of view of constructing weak solutions through a fully discretized approach. In this treatment, we consider simplified Dirichlet type boundary conditions in both the elastic displacement and pressure variables and give a full treatment of weak solutions. Our construction of weak solutions for the nonlinear problem is based on a priori estimates, a requisite feature in addressing the nonlinearity. We utilize a spatial semi-discretization and employ a multi-valued fixed point argument for a clear construction of weak solutions. We also provide regularity criteria for uniqueness of solutions.
