Partner: Markus Kunze

University of Konstanz (DE)

Ostatnie publikacje
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.

Słowa kluczowe:

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

Afiliacje autorów:

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