Fast Reaction Limits via $$\Gamma $$-Convergence of the Flux Rate Functional

Abstract We study the convergence of a sequence evolution equations for measures supported on nodes graph. The themselves can be interpreted as forward Kolmogorov Markov jump processes, or equivalently concentrations in network linear reactions. rates reaction are divided two classes; ‘slow’ constant, and ‘fast’ scaled $$1/\epsilon $$ 1 / ? , we prove fast-reaction limit $$\epsilon \rightarrow 0$$ ? 0 . establish $$\Gamma ? -convergence result rate functional terms both concentration at each node flux over edge (the level-2.5 function). limiting system is again described by functional, characterises fast slow fluxes system. This method proof has three advantages. First, no condition detailed balance required. Secondly, formulation leads to short simple -convergence; price pay more involved compactness proof. Finally, deals with approximate solutions, which not zero but small, without any changes.