Exact solutions to nonlinear equations describing a flow of suspension in a porous medium / *N. E. Leont'ev, D. A. Tatarenkova.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 3. P. 49-54
[Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 61-65].

The general solution to a nonlinear system of differential equations describing one-dimensional flows of a low-concentrated suspension through a porous medium with consideration of particle deposition is constructed. A number of closed-form solutions are specified in terms of elementary functions. The formation of non-physical singularities is studied.

*Key words*:
flow through a porous medium, suspension, deep bed filtration, particle
deposition, gradient catastrophe.