Weak solutions to stochastic porous media equations

Abstract

A stochastic version of the porous medium equation is studied. The corresponding Kolmogorov equation is solved in a space \(L^{2}(H, \nu)\) where ν is an invariant measure. Then a weak solution, that is a solution in the sense of the corresponding martingale problem, is constructed.

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Correspondence to Giuseppe Da Prato or Michael Röckner.

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Da Prato, G., Röckner, M. Weak solutions to stochastic porous media equations. J.evol.equ. 4, 249–271 (2004). https://doi.org/10.1007/s00028-003-0140-9

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Mathematics Subject Classification (2000):

  • 76S05
  • 35J25
  • 37L40