Stochastic porous media equations in Rd

摘要: Abstract Existence and uniqueness of solutions to the stochastic porous media equation d X − Δ ψ ( ) t = W in R are studied. Here, is a Wiener process, maximal monotone graph × such that r ≤ C | m , ∀ ∈ . In this general case, dimension restricted ≥ 3 main reason being absence convenient multiplier result space H { φ S ′ ; ξ F L 2 } for When Lipschitz, well-posedness, however, holds all dimensions on classical Sobolev 1 If ρ + we prove finite time extinction with strictly positive probability.