Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities

Röckner M, Wu W, Xie Y. Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities. Stochastic Processes and their Applications. 2018;128(6):2131-2151.We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space (E, B(E), mu), and the Laplacian replaced by a negative definite self-adjoint operator L. In the case of Lipschitz nonlinearities Psi, we in particular generalize previous results for open E subset of R-d and L=Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on L, in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of Psi at infinity for L-2(mu)-initial data. (C) 2017 Elsevier B.V. All rights reserved