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 $1/2$.

arXiv comment25 pages, small changes according to the published version

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• Porous media equations with multiplicative space-time white noise
• Ergodicity for Stochastic Porous Media Equations
• Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
• Optimal regularity in time and space for stochastic porous medium equations
• Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality
• Numerical approximation of singular-degenerate parabolic stochastic PDEs
• Large deviations for stochastic porous media equations
• The obstacle problem for stochastic porous media equations
• Noise and Stability in Reaction-diffusion Equations