Weierstraß-Institut für Angewandte Analysis und Stochastik On the evolutionary Γ-convergence of gradient systems modeling slow and fast chemical reactions

Karoline Disser, Matthias Liero, Jonathan Zinsl
2010 Mathematics Subject Classification. 34E15, 49J40, 49J45, 80A30, 92E20   unpublished
We investigate the limit passage for a system of ordinary differential equations modeling slow and fast chemical reaction of mass-action type, where the rates of fast reactions tend to infinity. We give an elementary proof of convergence to a reduced dynamical system acting in the slow reaction directions on the manifold of fast reaction equilibria. Then we study the entropic gradient structure of these systems and prove an E-convergence result via Γ-convergence of the primary and dual
more » ... y and dual dissipation potentials, which shows that this structure carries over to the fast reaction limit. We recover the limit dynamics as a gradient flow of the entropy with respect to a pseudo-metric.