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Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. (English) Zbl 1162.76054

Summary: This paper addresses the existence and uniqueness of strong solutions to stochastic porous media equations \(dX - \Delta \Psi (X) dt=B(X) dW(t)\) in bounded domains of \(\mathbb R^d\) with Dirichlet boundary conditions. Here \(\Psi \) is a maximal monotone graph in \(\mathbb R\times \mathbb R\) (possibly multivalued) with the domain and range all of \(\mathbb R\). Compared with the existing literature on stochastic porous media equations, no growth condition on \(\Psi \) is assumed and the diffusion coefficient \(\Psi \) might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition.

MSC:

76S05 Flows in porous media; filtration; seepage
76M35 Stochastic analysis applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics

References:

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