Entropy solutions for stochastic porous media equations

We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and $L_1$-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators $\mathrm{\Delta }(|u{|}^{m?1}u)$ for all $m\in (1,\infty )$, and Hölder continuous diffusion nonlinearity with exponent 1/2.