Entropy solutions for stochastic porous media equations

Abstract

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 $\Delta (|u{|}^{m-1}u)$ for all $m\in (1,\infty )$, and Hölder continuous diffusion nonlinearity with exponent $1/2$.

25 pages, small changes according to the published version