Finite speed of propagation for stochastic porous media equations
Abstract
We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative spacetime rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are then used to prove that the corresponding random attractor has infinite fractal dimension.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1210.2415
 Bibcode:
 2012arXiv1210.2415G
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 Mathematics  Dynamical Systems;
 37L55;
 60H15 (Primary) 76S05;
 37L30 (Secondary)
 EPrint:
 26 pages