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arXiv · 1803.06953

Entropy solutions for stochastic porous media equations

Konstantinos Dareiotis·Maté Gerencsér·Benjamin Gess
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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 H\"older continuous diffusion nonlinearity with exponent $1/2$.

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BibTeXRIS

Konstantinos Dareiotis, Maté Gerencsér, Benjamin Gess. 2018-03-19. Entropy solutions for stochastic porous media equations. https://doi.org/10.1016/j.jde.2018.09.012

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