INVARIANCE OF SUBSPACES UNDER THE SOLUTION FLOW OF SPDE
Wei Liu · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2010
In this paper we investigate some regularity property for the solution to SPDE. Under certain assumptions we prove that the solution of an SPDE takes values in some subspace of the original state space if the initial condition does so. As examples, the main result is applied to different types of SPDE such as stochastic reaction-diffusion equations, the stochastic p-Laplace equation, stochastic porous media and fast diffusion equations in Hilbert space.