SVI solutions to stochastic nonlinear diffusion equations on general measure spaces.

We establish a framework for the existence and uniqueness of solutions to stochastic nonlinear (possibly multi-valued) diffusion equations driven by multiplicative noise, with the drift operator L being the generator of a transient Dirichlet form on a finite measure space (E , B , μ) and the initial value in F e ∗ , which is the dual space of an extended transient Dirichlet space. L and F e ∗ replace the Laplace operator Δ and H - 1 , respectively, in the classical case. This framework includes stochastic fast diffusion equations, stochastic fractional fast diffusion equations, the Zhang model, and applies to cases with E being a manifold, a fractal, or a graph. In addition, our results apply to operators - f (- L) , where f is a Bernstein function, e.g., f (λ) = λ α or f (λ) = (λ + 1) α - 1 , 0 < α < 1 . [ABSTRACT FROM AUTHOR]