Mihály Kovács, Eszter Sikolya
Published 2020-11-23Version 1
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.
Exact controllability of stochastic parabolic equations with multiplicative noise
Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise
Existences and upper semi-continuity of pullback attractors in $H^1(\mathbb{R}^N)$ for non-autonomous reaction-diffusion equations perturbed by multiplicative noise
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