ON THE CAUCHY PROBLEM FOR DEGENERATE EQUATIONS OF A REACTING GAS MIXTURE

Abstract

In this article, a system of nonlinear differential equations describing the one-dimensional flow of a reacting mixture of gases in a porous medium is investigated. An unlimited domain is considered. Moreover, the desired functions tend to zero at the initial moment of time, which leads to the degeneracy of the equations. The Cauchy problem for the equations describing flow of a reacting mixture of gases is considered. At the initial time all medium characteristics are know and have various limits at infinity. A system of differential equations is investigated that describes a one-dimensional unsteady flow of a reacting gas mixture. We study the Cauchy problem with degenerate initial data corresponding to one problem. Moreover, the desired functions at the initial moment of time have about one problem at infinity. A feature of flows with finite viscosity is the absence of shock waves in them, i.e. except for the contact, there can be no other strong gap. The existence of a generalized solution is proved by the method of regularization.