In this note, we extend the problem treated in (Lok, Math Modelling Anal 24:617–634 (2019)) to the case of permeable surface which is shrinking in mutually orthogonal directions. Both numerical and asymptotic solutions are obtained for two important governing parameters, \(\gamma \) the shrinking rate and S characterizing the fluid transfer through the boundary. In this problem, a restriction on S is required for a solution to exist. This contrasts with the problem in (Lok, Math Modelling Anal 24:617–634 (2019)) where no restriction on S is needed. Numerical solutions show that for a fixed value of S, two critical points \(\gamma _c\) are observed for \(S > 2\). Conversely, two critical points \(S_c\) are found for a given value of \(\gamma \) when \(S > 2\). A discussion on the nonexistence of solution for \(S = 2\) is given and asymptotic solutions for S large and \((S-2)\) small are also presented.

在本说明中，我们将（Lok，Math Modeling Anal 24：617-634（2019））中处理的问题扩展到在相互正交的方向上收缩的可渗透表面的情况。用于两个重要的管理参数同时获得的数值和渐近解，\（\伽马\）的收缩率和小号表征通过边界的流体转移。在此问题中，要使解存在就需要对S进行限制。这与（Lok，Math Modeling Anal 24：617–634（2019））中的问题相反，该问题不需要对S进行限制。数值解表明，对于S的固定值，对于\（S> 2 \）观察到两个临界点\（\ gamma _c \）。相反，当\（S> 2 \）时，对于给定的\（\ gamma \）值，发现了两个临界点\（S_c \）。讨论了\（S = 2 \）解的不存在性，并给出了S大和\（（S-2）\）小的渐近解。