Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability models provide a mechanics-based approach to describe hydrodynamics in aforesaid porous materials. However, current theoretical results primarily address state-state response, and their counterparts in the transient regime are still wanting. The primary aim of this paper is to fill this knowledge gap. We present three principal properties -- with rigorous mathematical arguments -- that the solutions under the double porosity/permeability model satisfy in the transient regime: backward-in-time uniqueness, reciprocity, and a variational principle. We employ the ``energy method'' -- by exploiting the physical total kinetic energy of the flowing fluid -- to establish the first property and Cauchy-Riemann convolutions to prove the next two. The results reported in this paper -- that qualitatively describe the dynamics of fluid flow in double-pored media -- have (a) theoretical significance, (b) practical applications, and (c) considerable pedagogical value. In particular, these results will benefit practitioners and computational scientists in checking the accuracy of numerical simulators. The backward-in-time uniqueness lays a firm theoretical foundation for pursuing inverse problems in which one predicts the prescribed initial conditions based on data available about the solution at a later instance.

翻译：理解多孔材料中的流体运动对能源安全与生理学至关重要。例如，页岩（地质材料）和骨骼（生物材料）均呈现出多孔网络结构。双重孔隙/渗透率模型提供了基于力学的方法来描述上述多孔材料中的流体动力学。然而，当前理论成果主要针对稳态响应，其在瞬态领域的研究仍存在空白。本文的主要目标正是填补这一认知缺口。我们通过严格的数学论证，提出了双重孔隙/渗透率模型解在瞬态领域满足的三项基本性质：时间逆向唯一性、互易性及变分原理。利用流动流体的物理总动能这一"能量法"建立第一项性质，并通过柯西-黎曼卷积方法证明后两项性质。本文所报道的定性描述双孔介质中流体动力学的结果具有：(a) 理论重要性，(b) 实际应用价值，以及(c) 显著的教学意义。具体而言，这些成果将有助于实践者和计算科学工作者检验数值模拟器的准确性。时间逆向唯一性为开展逆问题研究奠定了坚实的理论基础——这类问题需基于后期时刻的解数据反推预设初始条件。