Weak Solutions to the Equations of Motion of Viscous Compressible Reacting Binary Mixtures: Uniqueness and Lipschitz-Continuous Dependence on Data

Abstract

1. An extensive literature is devoted to systems of quasilinear equations of motion of viscous compressible media (see [1, 2]). One of the problems of current interest is the development of the theory of global (with respect to time and data) weak solutions, including questions of their existence, uniqueness, and continuous dependence on data (such as initial data, the coefficients of the equations, the constant terms, etc.). For the system of equations of one-dimensional motion of a viscous heat-conducting gas, the last two questions were studied in [3–6] (see also [7, 8]). For more complicated systems of equations for reacting gases (in other words, in combustion problems) weak solutions were studied in [9, 10]. Quite recently, in [11], the existence of weak solutions was obtained for an even more complicated system of equations, namely, for a reacting binary gas mixture. Note that regular solutions of problems concerning binary mixtures were studied earlier in [12, 13]. The present paper is devoted to the questions of uniqueness of these weak solutions and of their continuous dependence on data. The system of quasilinear equations of one-dimensional motion of a viscous compressible reacting binary gas mixture is of the form