Exact solutions to one-dimensional problem of oil displacement by chemical

We consider the displacement of oil by water with active chemical reagents in porous media. A one-dimensional model of reagent transport and deposition is defined by a hyperbolic system of first-order equations. The purpose of the article is to find the conditions for the existence of a continuous solution with discontinuous boundary and initial conditions. The method of characteristics allows constructing solutions for both continuous and discontinuous initial and boundary conditions. Solutions of the system for the Cauchy problem in a half-plane and for the initial–boundary value problem are found. The properties of solutions on discontinuity lines are studied. Sufficient conditions for the continuity of solutions are obtained. Examples of continuous and discontinuous solutions are given.