Entropy solutions for stochastic porous media equations
- Authors: Konstantinos Dareiotis, Maté Gerencsér, Benjamin Gess
- Preprint year: 2018
- First public date: 2018-03-19
- arXiv: 1803.06953
- Status: Published
- Publication type: Journal article
- Publication year: 2019
- Journal: Journal of differential equations, 266 (2019) 6, pp. 3732-3763
- DOI: 10.1016/j.jde.2018.09.012
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 $1/2$.