Stochastic reaction–diffusion equations on networks
Journal article, 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


Mihaly Kovacs

Chalmers, Mathematical Sciences

Pázmány Péter Catholic University

Eszter Sikolya

Eötvös Loránd University (ELTE)

Hungarian Academy of Sciences

Journal of Evolution Equations

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

Vol. In Press

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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