Entropy solutions for stochastic porous media equations

@article{Dareiotis2018EntropySF,
  title={Entropy solutions for stochastic porous media equations},
  author={Konstantinos Dareiotis and M{\'a}t{\'e} Gerencs{\'e}r and Benjamin Gess},
  journal={Journal of Differential Equations},
  year={2018},
  volume={266},
  pages={3732-3763}
}
  • Konstantinos Dareiotis, Máté Gerencsér, Benjamin Gess
  • Published 2018
  • Mathematics
  • Journal of Differential 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 Δ ( | u | m − 1 u ) for all m ∈ ( 1 , ∞ ) , and Holder continuous diffusion nonlinearity with exponent 1/2. 

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