On the stochastic Allen–Cahn equation on networks with multiplicative noise
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 7,p. 1-24
- https://doi.org/10.14232/ejqtde.2021.1.7
Abstract
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.Keywords
This publication has 34 references indexed in Scilit:
- Asymptotic state lumping in transport and diffusion problems on networks with applications to population problemsMathematical Models and Methods in Applied Sciences, 2015
- Semigroup approach to diffusion and transport problems on networksSemigroup Forum, 2015
- Stochastic FitzHugh-Nagumo equations on networks with impulsive noiseElectronic Journal of Probability, 2008
- Chapter 1 Semigroups and evolution equations: Functional calculus, regularity and kernel estimatesPublished by Elsevier BV ,2002
- Dynamical interface transition in ramified media with diffusionCommunications in Partial Differential Equations, 1996
- Front propagation for reaction-diffusion equations of bistable typeAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1992
- Sturm‐Liouville eigenvalue problems on networksMathematical Methods in the Applied Sciences, 1988
- Classical solvability of linear parabolic equations on networksJournal of Differential Equations, 1988
- A characteristic equation associated to an eigenvalue problem on c2-networksLinear Algebra and its Applications, 1985
- A microscopic theory for antiphase boundary motion and its application to antiphase domain coarseningActa Metallurgica, 1979