The minimum entropy principle for a two‐phase flow model

Abstract

Bounded entropy solutions of the Baer-Nunziato model of two-phase flows are proved to satisfy the minimum entropy principle; that is, the spatial infimum of the specific entropy inf x S(u(x, t)) is an increasing function of time. The model was derived for the study of deflagration-to-detonation transition in granular explosives and consists of seven nonlinear partial differential equations with nonconservative source terms. Apparently, we will also show that the generalized entropy inequality can be reduced in the usual divergence form for standard entropy pairs in gas dynamics equations.