Stochastic reaction–diffusion equations on networks
Artikel i vetenskaplig tidskrift, 2021

We consider stochastic reaction–diffusion equations on a finite network represented by a finite graph. On each edge in the graph, a multiplicative cylindrical Gaussian noise-driven reaction–diffusion equation is given supplemented by a dynamic Kirchhoff-type law perturbed by multiplicative scalar Gaussian noise in the vertices. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. We utilize the semigroup approach for stochastic evolution equations in Banach spaces to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. In order to do so, we generalize existing results on abstract stochastic reaction–diffusion equations in Banach spaces.

stochastic FitzHugh–Nagumo equation

Stochastic reaction–diffusion equations on networks

Analytic semigroups

Stochastic evolution equations

Författare

Mihaly Kovacs

Chalmers, Matematiska vetenskaper

Pázmány Péter Katolikus Egyetem

Eszter Sikolya

Eötvös Loránd University (ELTE)

Magyar Tudomanyos Akademia

Journal of Evolution Equations

1424-3199 (ISSN) 1424-3202 (eISSN)

Vol. In Press

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1007/s00028-021-00719-w

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Senast uppdaterat

2021-06-30