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Stochastic FitzHugh-Nagumo equations on networks with impulsive noise

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Stochastic FitzHugh-Nagumo equations on networks with impulsive noise
2.	Creator	Author's name, affiliation, country	Stefano Bonaccorsi; Università di Trento
2.	Creator	Author's name, affiliation, country	Carlo Marinelli; Universität Bonn
2.	Creator	Author's name, affiliation, country	Giacomo Ziglio; Università di Trento
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stochastic PDEs, FitzHugh-Nagumo equation, Lévy processes, maximal monotone operators
3.	Subject	Subject classification	60H15, 60J75, 47H06, 92C20
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG; EU
7.	Date	(YYYY-MM-DD)	2008-08-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/532
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-532
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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