We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and L1-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators ∆ (| u| m - 1 u) for all m ∈ (1 , ∞), and Hölder continuous diffusion nonlinearity with exponent 1/2.
Journal of Differential Equations
- Pub Date:
- March 2019
- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- 25 pages, small changes according to the published version