An averaging principle for fast diffusions in domains separated by semi-permeable membranes
- Speaker(s)
- Adam Bobrowski
- Affiliation
- Politechnika Lubelska
- Date
- April 21, 2016, 12:30 p.m.
- Room
- room 4060
- Seminar
- Seminar of Mathematical Physics Equations Group
We prove an averaging principle which asserts convergence of
diffusions on domains separated by semi-permeable membranes, when the
speed of diffusion tends 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 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, including models of neurotransmitters, kinaze
activity and intracellular calcium dynamics. This is a joint work with
B. Kazmierczak and M. Kunze.