Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions
Probability
2017-02-17 v1
Abstract
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product Hilbert space, for which we prove the existence and uniqueness of a mild solution. Eventually, a stochastic optimal control application is studied.
Cite
@article{arxiv.1702.04947,
title = {Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions},
author = {Francesco Cordoni and Luca Di Persio},
journal= {arXiv preprint arXiv:1702.04947},
year = {2017}
}