An averaging principle for fast diffusions in domains separated by semi-permeable membranes

作者：Bobrowski Adam^*; Kazmierczak Bogdan; Kunze Markus

来源：Mathematical Models and Methods in Applied Sciences, 2017, 27(4): 663-706.

DOI：10.1142/S0218202517500130

• 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

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.

• 出版日期2017-4