Nazaikinskii, V.E.Bedrikovetsky, P.G.Kuzmina, L.I.Osipov, Y.V.2025-07-292025-07-292020SIAM Journal on Applied Mathematics, 2020; 80(5):2120-21430036-13991095-712Xhttps://hdl.handle.net/2440/146410An 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 suffcient coefficient condition for the unique solvability of the problem is derived.en© 2020 Society for Industrial and Applied Mathematicsdeep bed filtration; quasilinear hyperbolic system; method of characteristics; exact solution; unique solvabilityJournal article10.1137/19M1309195557564Bedrikovetsky, P.G. [0000-0002-4786-8275] [0000-0002-7100-3765] [0000-0003-2909-6731]