Abstract
This paper addresses the existence and uniqueness of strong solutions to stochastic porous media equations dX−ΔΨ(X) dt=B(X) dW(t) in bounded domains of ℝd with Dirichlet boundary conditions. Here Ψ is a maximal monotone graph in ℝ×ℝ (possibly multivalued) with the domain and range all of ℝ. Compared with the existing literature on stochastic porous media equations, no growth condition on Ψ is assumed and the diffusion coefficient Ψ might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition.
Citation
Viorel Barbu. Giuseppe Da Prato. Michael Röckner. "Existence of strong solutions for stochastic porous media equation under general monotonicity conditions." Ann. Probab. 37 (2) 428 - 452, March 2009. https://doi.org/10.1214/08-AOP408
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