The classifications and reductions of radially symmetric diffusion system are studied due to the conditional Lie-Bäcklund symmetry method. We obtain the invariant condition, which is the so-called determining system and under which the radially symmetric diffusion system admits second-order conditional Lie-Bäcklund symmetries. The governing systems and the admitted second-order conditional Lie-Bäcklund symmetries are identified by solving the nonlinear determining system. Exact solutions of the resulting systems are constructed due to the compatibility of the original system and the admitted differential constraint corresponding to the invariant surface condition. For most of the cases, they are reduced to solving four-dimensional dynamical systems.

中文翻译：

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径向对称扩散系统的二阶条件Lie-Bäcklund对称性和微分约束

由于条件Lie-Bäcklund对称方法，研究了径向对称扩散系统的分类和简化。我们得到不变条件，即所谓的确定系统，在该条件下径向对称扩散系统允许二阶条件Lie-Bäcklund对称。通过求解非线性确定系统，可以确定控制系统和允许的二阶条件Lie-Bäcklund对称性。由于原始系统的兼容性以及与不变的表面条件相对应的允许的差分约束，因此构造了所得系统的精确解。对于大多数情况，它们被简化为求解二维动力学系统。