| Título: | Stochastic FitzHugh-Nagumo equations on networks with impulsive noise |
| Autores: |
Bonaccorsi, Stefano; Università di Trento Marinelli, Carlo; Universität Bonn Ziglio, Giacomo; Università di Trento |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Stochastic PDEs, FitzHugh-Nagumo equation, Lévy processes, maximal monotone operators 60H15, 60J75, 47H06, 92C20 |
| Descripción: | 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. |
| Idioma: | No aplica |
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