Abstract. In this paper we study mixture of gases, each governed by a gamma law. The system is modeled by the p-system with variable gamma. We use this model to study immiscible gas flow. The main result is that the Cauchy problem with large data is shown to have a solution. We use the Glimm scheme for the proof. The result is illustrated by numerical examples.
Abstract. In this paper we study front tracking for a model of one dimensional, immiscible flow of several isentropic gases, each governed by a gammalaw. The model consists of the p-system with variable gamma representing the different gases. The main result is the convergence of a front tracking algorithm to a weak solution, thereby giving existence as well. This convergence holds for general initial data with a total variation satisfying a specific bound. The result is illustrated by numerical examples.
We study the global existence of spatially periodic solutions for certain models of gas flow in Lagrangian coordinates for which the pressure has the form [Formula: see text], where v, as usual, is the specific volume, and [Formula: see text], [Formula: see text] are smooth functions of the variable coefficient [Formula: see text], which is assumed to satisfy suitable smoothness and decay properties, in particular, [Formula: see text], uniformly, as t →0. One important feature of our analysis is that the initial total variation over one period may be taken as large as we wish as long as [Formula: see text] is sufficiently close to 1. We also prove a non-homogeneous entropy inequality which implies the decay of the solution to the mean value as t → ∞.
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