Stochastic partial differential equations with additive noise on time-varying domains

Stochastic partial differential equations (SPDE) with additive noise of the reaction-diffusion type are formulated on time-varying domains, where the domains are obtained by a regular temporally dependent spatially diffeomorphic transformation of a reference domain, which is bounded and has a smooth boundary. The main issue considered here is the interpretation of the notions of noise and solution on time-varying domains.