@article{EJP532,
author = {Stefano Bonaccorsi and Carlo Marinelli and Giacomo Ziglio},
title = {Stochastic FitzHugh-Nagumo equations on networks with impulsive noise},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Stochastic PDEs, FitzHugh-Nagumo equation, Lévy processes, maximal monotone operators},
abstract = {We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons. Motivated by the discussion in the biological literature, we impose a general diffusion equation on each edge through a generalized version of the FitzHugh-Nagumo model, while the noise acting on the boundary is described by a generalized stochastic Kirchhoff law on the nodes. In the abstract framework of matrix operators theory, we rewrite this stochastic boundary value problem as a stochastic evolution equation in infinite dimensions with a power-type nonlinearity, driven by an additive Lévy noise. We prove global well-posedness in the mild sense for such stochastic partial differential equation by monotonicity methods.},
pages = {no. 49, 1362-1379},
issn = {1083-6489},
doi = {10.1214/EJP.v13-532},
url = {http://ejp.ejpecp.org/article/view/532}}