The large-time asymptotics of weak solutions to Maxwell–Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither symmetric nor positive definite, but the equations admit a formal gradient-flow structure which provides entropy (free energy) estimates. The main result is the exponential decay to the unique equilibrium with a rate that is constructive up to a finite-dimensional inequality. The key elements of the proof are the existence of a unique detailed-balance equilibrium and the derivation of an inequality relating the entropy and the entropy production. The main difficulty comes from the fact that the reactions are represented by molar fractions while the conservation laws hold for the concentrations. The idea is to enlarge the space of n partial concentrations by adding the total concentration, viewed as an independent variable, thus working with $$n+1$$ n + 1 variables. Further results concern the existence of global bounded weak solutions to the parabolic system and an extension of the results to complex-balance systems.

中文翻译：

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Maxwell-Stefan 型反应交叉扩散系统解的指数时间衰减

研究了具有不同摩尔质量和可逆反应的化学反应流体的 Maxwell-Stefan 扩散系统的弱解的大时间渐近性。系统的扩散矩阵通常既不是对称的也不是正定的，但方程承认提供熵（自由能）估计的正式梯度流结构。主要结果是指数衰减到唯一均衡，其速率对于有限维不等式是建设性的。证明的关键要素是唯一的详细平衡均衡的存在以及与熵和熵产生相关的不等式的推导。主要困难来自这样一个事实，即反应由摩尔分数表示，而守恒定律适用于浓度。这个想法是通过添加总浓度来扩大 n 部分浓度的空间，被视为一个自变量，从而使用 $$n+1$$n+1 个变量。进一步的结果涉及抛物线系统的全局有界弱解的存在以及将结果扩展到复杂平衡系统。