Asymptotic stability of a composite wave to the one-dimensional compressible Navier-Stokes equations for a reacting mixture

Abstract

This paper is concerned with the large time behavior of solutions for the Cauchy problem to the compressible Navier-Stokes equations for a reacting mixture with zero viscosity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves and contact discontinuity, it is shown that the composition of two rarefaction waves with a viscous contact wave is asymptotically stable, while the strength of the composite wave and the initial perturbation are suitably small.