The mathematical model of filtration consolidation process of porous medium is investigated under salt transfer influence. The mathematical model is described by a boundary-value problem in the domain with free boundary for the system of two quasi-linear parabolic equations. On the free moving boundary, an integral kinematic boundary condition is set. The existence and uniqueness of the local in time solution of one-dimensional problem in Hölder spaces is proved.

quasi-linear equations of parabolic type, system, free mobile boundary, existence and uniqueness of solution.