Random attractors via pathwise mild solutions for stochastic parabolic evolution equations
Abstract
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution problems in Banach spaces with additive noise and prove the existence of random exponential attractors. These are compact random sets of finite fractal dimension that contain the global random attractor and are attracting at an exponential rate. In order to apply the framework of random dynamical systems, we use the concept of pathwise mild solutions. This approach is essential for our setting since the stochastic evolution equation cannot be transformed into a family of PDEs with random coefficients via the stationary OrnsteinUhlenbeck process.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.02787
 arXiv:
 arXiv:2006.02787
 Bibcode:
 2020arXiv200602787K
 Keywords:

 Mathematics  Probability;
 60H15;
 37H05;
 37L55
 EPrint:
 32 pages, preprint