Kru\v{z}kov-type uniqueness theorem for the chemical flood conservation law system with local vanishing viscosity admissibility

Abstract

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 piece-wise $\mathcal C^1$-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 Lagrange 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 Kru\v{z}kov's theorem.