The paper deals with Barenblat’s model of non-stationary two-phase filtration of oil and water with active reagents. This model describes frontal It is described by the first order hyperbolic system of two nonlinear partial differential equations. We show that this system is equivalent to the symplectic Monge–Ampe` re equation. In the case of carbonized water this equation is contact equivalent to the linear wave equation. This gives us a possibility to construct exact multivalued solutions of Barenblat’s equations.