Decay rate to contact discontinuities for the one-dimensional compressible Euler-Fourier system with a reacting mixture

Abstract

In this paper, we investigate the nonlinear stability of contact waves to the Cauchy problem of the compressible Euler-Fourier system with a reacting mixture in one dimension under the non-zero mass condition. If the corresponding Riemann problem for the compressible Euler system admits a contact discontinuity solution, it is shown that the contact wave is nonlinearly stable, while the strength of the contact discontinuity and the initial perturbation are suitably small. Especially, we obtain the decay rate of contact waves by using anti-derivative methods and elaborated energy estimates.