We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

我们研究了非线性偏微分方程组的数学特性，这些方程组描述了在某些简化假设下水饱和粒状材料中的演化过程。在活化发生之前，未固结的固体基质表现为理想的塑料材料，然后开始以牛顿流体或广义牛顿流体的形式流动。塑性屈服应力不是恒定的，并且取决于给定的岩石静压力与孔隙空间中流体压力之间的差。我们研究在不透水容器中的不稳定三维流动，该流动受粘滑边界条件的影响。在对数据的现实假设下，我们建立了长期的大数据存在理论。