Before revision:  We study the convergence of the  total mass of a solution to this stochastic initial-boundary value problem when the mean-reversion coefficients of the volatilities are multiples of a parameter that tends to infinity. When the volatilities of the volatilities are multiples of the square root of the same parameter, the convergence is extremely weak .
After revision:  We study the convergence of the total mass of a solution to this stochastic initial-boundary value problem under fast mean reversion of the volatility. We consider two cases. In the first case the volatility converges to a limiting distribution and the convergence of the system is in the sense of weak convergence .