A Variational Approach to Neumann Stochastic Semi-Linear Equations Modeling the Thermostatic Control

Abstract

In the present paper, we prove existence and uniqueness of a mild solution for a stochastic semi-linear equation with Neumann boundary conditions, using only general monotonicity assumptions. The study of this equation is motivated by physical applications as the model of the temperature control through the boundary. The result is proved by using an optimal control approach based on the variational principle of Brezis and Ekeland.