Convergence of solutions for the stochastic porous media equations and homogenization

This work addresses the stochastic porous media equation with multiplicative noise and diffusivity function depending on the space variable. The first part of the paper proves an existence and uniqueness result for this type of equation, the second part proves the convergence of the solutions in the case of graph convergence of the porous media operator, and this result is used in the third part for an homogenization theorem.