An averaging principle for fast diffusions in domains separated by semi-permeable membranes
arXiv:1603.00494 · doi:10.1142/S0218202517500130
Abstract
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 towards the end of the paper.
34 pages, 6 figures; revised version of the article which was restructured and now contains a section explaining the general idea and the used mathematical tools to make the article more accessible to a broader audience. The main results are unchanged