Stochastic FitzHugh-Nagumo equations on networks with impulsive noise
| dc.creator | Bonaccorsi, Stefano | |
| dc.creator | Marinelli, Carlo | |
| dc.creator | Ziglio, Giacomo | |
| dc.date | 2007-12-04 | |
| dc.date | 2008-08-09 | |
| dc.date.accessioned | 2026-07-07T09:55:29Z | |
| dc.date.available | 2026-07-07T09:55:29Z | |
| dc.description | 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. | |
| dc.description | 18 pages. Minor revision | |
| dc.identifier | https://arxiv.org/abs/0712.0580 | |
| dc.identifier | http://arxiv.org/abs/0712.0580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166645 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Probability | |
| dc.title | Stochastic FitzHugh-Nagumo equations on networks with impulsive noise | |
| dc.type | text |