Institute of Fundamental Technological Research
Polish Academy of Sciences


Markus Kunze

University of Konstanz (DE)

Recent publications
1.  Bobrowski A., Kaźmierczak B., Kunze M., An averaging principle for fast diffusions in domains separated by semi-permeable membranes, MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, ISSN: 0218-2025, DOI: 10.1142/S0218202517500130, Vol.27, No.4, pp.663-706, 2017

We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain's intensities are proportional to the membranes' permeability and inversely proportional to the domains' sizes. Analytically, the limit is an example of a singular perturbation in which boundary and transmission conditions play a crucial role. This averaging principle is strongly motivated by recent signaling pathways models of mathematical biology, which are discussed toward the end of the paper.

Convergence of sectorial forms and of semigroups of operators, diffusion processes, boundary and transmission conditions, Freidlin–Wentzell averaging principle, singular perturbations, signaling pathways, kinase activity, intracellular calcium dynamics, neurotransmitters

Bobrowski A. - Lublin University of Technology (PL)
Kaźmierczak B. - IPPT PAN
Kunze M. - University of Konstanz (DE)

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