Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions

2017/02/16 by Francesco Cordoni, Cordoni, Francesco, Luca Di Persio +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.PR

paper · pdf · doi:10.48550/arxiv.1702.04947

arxiv created 2017/02/16 · arxiv updated 2017/02/17

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.

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