• Media type: Text; E-Book; Report
  • Title: On the evolutionary Gamma-convergence of gradient systems modeling slow and fast chemical reactions
  • Contributor: Disser, Karoline [Author]; Liero, Matthias [Author]; Zinsl, Jonathan [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2016
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2227
  • Keywords: 49J45 ; 34E15 ; 49J40 ; article ; Gradient systems -- mass-action law -- dissipation potential -- energy dissipation balance -- multiscale evolution problems -- reversible reaction kinetics -- Gamma-convergence ; 80A30 ; 92E20
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  • Description: 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 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.