Kružkov-type uniqueness theorem for the chemical flood conservation law system with local vanishing viscosity admissibility

In this paper, we study the uniqueness of solutions of the initial-boundary value problem in the quarter-plane for the chemical flood conservation law system in the class of piecewise [Formula: see text]-smooth functions under certain restrictions. The vanishing viscosity method is used locally on the discontinuities of the solution to determine admissible and inadmissible shocks. The Lagrangian coordinate transformation is utilized in order to split the equations. The proof of uniqueness is based on an entropy inequality similar to the one used in the classical Kružkov’s theorem.