SIAM Journal on Applied Mathematics, Volume 80, Issue 5, Page 2120-2143, January 2020.
An initial-boundary value problem for a quasilinear system describing deep bed filtration of a monodisperse suspension in a medium with pores of various sizes is investigated analytically. The filtration function is assumed to have power-law type while tending to zero with the power index lower than one. We found that this assumption has two consequences: (i) the blocking time is finite, and (ii) the characteristics issuing from the points where the retained particle concentration reaches its maximum are not uniquely determined. The exact solution is constructed by a modified method of characteristics, which removes the ambiguity by using an additional blocking line equation derived from the original problem. The weak singularity of the solution on the blocking line is described. A simple sufficient coefficient condition for the unique solvability of the problem is derived.

中文翻译：

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具有有限阻塞时间的深床过滤的精确解决方案

SIAM应用数学杂志，第80卷，第5期，第2120-2143页，2020年1月。
拟线性系统的初边值问题，该问题描述了具有各种尺寸孔的介质中单分散悬浮液的深床过滤。假设滤波函数具有幂律类型，而幂指数小于1时趋于零。我们发现该假设有两个结果：（i）阻塞时间是有限的，并且（ii）不能唯一确定从保留颗粒浓度达到最大值的点发出的特性。精确的解决方案是通过修改后的特征方法构造而成的，该方法通过使用从原始问题得出的附加阻塞线方程式消除了歧义。描述了阻塞线上溶液的弱奇异性。