On the stochastic allen–cahn equation on networks with multiplicative noise
Artikel i vetenskaplig tidskrift, 2021

We consider a system of stochastic Allen-Cahn equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative Gaussian noise driven stochastic Allen-Cahn equation is given with possibly different potential barrier heights supplemented by a continuity condition and a Kirchhoff-type law in the vertices. Using the semigroup approach for stochastic evolution equations in Banach spaces we obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. We also prove more precise space-time regularity of the solution.

Stochastic evolution equations

Stochastic reaction-diffusion equations on networks

Analytic semigroups

Stochastic Allen–Cahn equation


Mihaly Kovacs

Chalmers, Matematiska vetenskaper

Pázmány Péter Katolikus Egyetem

Eszter Sikolya

Magyar Tudomanyos Akademia

Eötvös Loránd University (ELTE)

Electronic Journal of Qualitative Theory of Differential Equations

1417-3875 (ISSN)

Vol. 2021 1-24 7



Sannolikhetsteori och statistik

Matematisk analys



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