Balance Laws and Transport Theorems for Flows with Singular Interfaces

This paper gives a concise but rigorous mathematical description of a material control volume that is separated into two parts by a singular surface at which physical states are discontinuous. The geometrical background material is summarized in a unified manner. Transport theorems for use in generic balance laws are given with proofs since they provide some insight into the results. Also the step from integral balances to differential equations is given in some detail.