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| This talk is on existence and uniqueness of solutions to the stochastic porous media equation dX-\Delta\psi(X) dt=X dW on \mathbb{R}^d. Here, W is a Wiener process and \psi is a maximal monotone graph in \mathbb{R}\times\mathbb{R} such that \psi(r)\le C(|r|^m+1), \forall r \in \mathbb{R}. In this general case the dimension is restricted to d\ge 3. When \psi is Lipschitz, the well-posedness, however, holds for all dimensions on the classical Sobolev space H^{-1}(\mathbb{R}^d). If \psi(r)r\ge \rho|r|^{m+1} and m:=\frac{d-2}{d+2}, we prove finite time extinction of the solutions with strictly positive probability. |
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