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2008 Stochastic FitzHugh-Nagumo equations on networks with impulsive noise
Stefano Bonaccorsi, Carlo Marinelli, Giacomo Ziglio
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Electron. J. Probab. 13: 1362-1379 (2008). DOI: 10.1214/EJP.v13-532


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.


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Stefano Bonaccorsi. Carlo Marinelli. Giacomo Ziglio. "Stochastic FitzHugh-Nagumo equations on networks with impulsive noise." Electron. J. Probab. 13 1362 - 1379, 2008.


Accepted: 25 August 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60075
MathSciNet: MR2438810
Digital Object Identifier: 10.1214/EJP.v13-532

Primary: 60H15
Secondary: 47H06 , 60J75 , 92C20

Keywords: FitzHugh-Nagumo equation , L&eacute , maximal monotone operators , stochastic PDEs , vy processes


Vol.13 • 2008
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