In this article, we consider diffusive transport of a reactive substance in a saturated porous medium including variable porosity. Thereby, the evolution of the microstructure is caused by precipitation of the transported substance. We are particularly interested in analysing the model when the equations degenerate due to clogging. Introducing an appropriate weighted function space, we are able to handle the degeneracy and obtain analytical results for the transport equation. Also the decay behaviour of this solution with respect to the porosity is investigated. There a restriction on the decay order is assumed, that is, besides low initial concentration also dense precipitation leads to possible high decay. We obtain nonnegativity and boundedness for the weak solution to the transport equation. Moreover, we study an ordinary differential equation (ODE) describing the change of porosity. Thereby, the control of an appropriate weighted norm of the gradient of the porosity is crucial for the analysis of the transport equation. In order to obtain global in time solutions to the overall coupled system, we apply a fixed point argument. The problem is solved for substantially degenerating hydrodynamic parameters.

中文翻译：

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堵塞多孔介质的扩散-降水模型中的退化方程

在本文中，我们考虑了活性物质在包括可变孔隙率在内的饱和多孔介质中的扩散传输。因此，微观结构的演变是由运输物质的沉淀引起的。当方程由于堵塞而退化时，我们对分析模型特别感兴趣。引入适当的加权函数空间，我们能够处理退化并获得输运方程的分析结果。还研究了该溶液相对于孔隙率的衰减行为。假设对衰减顺序有限制，即除了低初始浓度外，密集的降水也可能导致高衰减。我们得到了输运方程弱解的非负性和有界性。而且，我们研究了一个描述孔隙度变化的常微分方程（ODE）。因此，控制适当的孔隙度梯度加权范数对于输运方程的分析至关重要。为了获得整个耦合系统的全局及时解，我们应用了一个不动点参数。对于显着退化的流体动力学参数，该问题得到解决。