PUB - Publikationen an der Universität Bielefeld

Unique existence of solutions to porous media equations driven by continuous linear multiplicative space-time rough signals is proven for initial data in L-1(O). The generation of a continuous, order-preserving random dynamical system (RDS) on L-1(O) and the existence of a "small" random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. Uniform L-infinity bounds and uniform space-time continuity of solutions is shown. General noise including fractional Brownian Motion for all Hurst parameters is contained. A pathwise Wong-Zakai result for driving noise given by a continuous semimartingale is obtained. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.