|
|||||
|
|
Centre manifolds for stochastic evolution equations |
|
| Authors: | Xiaopeng Chen Anthony J Roberts Jinqiao Duan |
| Institution: | 1. Beijing International Center for Mathematical Research, Peking University, Beijing, Chinachenxiao002214336@outlook.com;3. School of Mathematical Sciences, University of Adelaide, Adelaide, Australia;4. Institute for Pure and Applied Mathematics (IPAM), University of California, Los Angeles, CA, USA;5. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA |
| Abstract: | Stochastic invariant manifolds are crucial in modelling the dynamical behaviour of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of centre manifolds for a class of stochastic evolution equations with linearly multiplicative noise are proved. The exponential attraction and approximation to centre manifolds are also discussed. |
| Keywords: | stochastic partial differential equations (spdes) exponential trichotomy centre manifolds stability dynamical approximation |