Details

Autor(en) / Beteiligte

• Barbu, Viorel
• Da Prato, Giuseppe
• Röckner, Michael

Titel

Existence of Strong Solutions for Stochastic Porous Media Equation under General Monotonicity Conditions

Ist Teil von

• The Annals of probability, 2009-03, Vol.37 (2), p.428-452

Ort / Verlag

Cleveland, OH: Institute of Mathematical Statistics

Erscheinungsjahr

2009

Link zum Volltext

Quelle

Project Euclid欧几里得数据库

Beschreibungen/Notizen

• 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 $\mathbb{R}^{d}$ with Dirichlet boundary conditions. Here Ψ is a maximal monotone graph in $\mathbb{R} x \mathbb{R}$ (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 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.