Abstract
We show that fast diffusions on finite graphs with semi permeable membranes on vertices may be approximated by finite-state Markov chains provided the related permeability coefficients are appropriately small. The convergence theorem involves a singular perturbation with singularity in both operator and boundary/transmission conditions, and the related semigroups of operators converge in an irregular manner. The result is motivated by recent models of synaptic depression.
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Communicated by Jan Derezinski
This research was supported by the Polish Government, grant number 6081/B/H03/2011/40.
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Bobrowski, A. From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping. Ann. Henri Poincaré 13, 1501–1510 (2012). https://doi.org/10.1007/s00023-012-0158-z
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DOI: https://doi.org/10.1007/s00023-012-0158-z