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Entropy solutions for stochastic porous media equations
Konstantinos Dareiotis, Maté Gerencsér, Benjamin Gess · 2018-03-19 · via math.PR updates on arXiv.org

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

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