The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary conditions. The global existence of very weak (integrable) solutions and the rigorous fast-reaction limit are proved. The limiting system inherits the entropy structure with an entropy that is not the sum of the entropies of the components. Uniform estimates are derived from the entropy inequality and the duality method.

中文翻译：

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交叉扩散系统和快速反应极限

研究了从具有已知熵的三种物种的反应交叉扩散系统到两个变量的交叉扩散系统的严格渐近性。在无磁通边界条件的有界域中研究方程。证明了极弱（可积分）解决方案的全局存在性和严格的快速反应极限。限制系统继承的熵结构的熵不是组件熵的总和。统一估计是从熵不等式和对偶方法得出的。