In this paper, we study the long-time behavior of the solutions for the initial-boundary value problem to a one-dimensional Navier–Stokes equations for a reacting mixture in a half line $\mathbb{R}_{+} := (0, \infty)$. We give the asymptotic stability of not only stationary solution for the impermeability problem but also the composite waves consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem of Navier–Stokes equations for a reacting mixture under some smallness conditions. The proofs are based on basic energy method.

中文翻译：

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反应混合物一维可压缩Navier-Stokes方程复合波的非线性稳定性

在本文中，我们研究了半线$ \ mathbb {R} _ {+}中一维反应混合物的一维Navier–Stokes方程的初边值问题解的长期行为。 （0，\ infty）$。我们给出了不渗透性问题的固定解的渐近稳定性，还给出了由纳音速BL-溶液，接触波和稀疏波组成的复合波的Navier–Stokes方程流入问题的渐近稳定性。细小条件。证明是基于基本能量法的。