We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation.

We forecast constraints on cosmological parameters in the interacting dark energy models using mock data generated for neutral hydrogen intensity mapping (IM) experiments. In this work, we only consider with transfer rate $Q=\beta H\rho_{\rm c}$, and take BINGO, FAST, SKA1-MID, Tianlai as typical examples of 21 cm IM find that cylinder array will play an important role constraining model. Assum...