NON-AUTONOMOUS STOCHASTIC EVOLUTION EQUATIONS, INERTIAL MANIFOLDS AND CHAFEE-INFANTE MODELS

Tóm tắt

Consider  a stochastic evolution equation containing  Stratonovich-multiplicative white noise  of the form  where the partial differential operator  is positive definite, self-adjoint with a discrete spectrum; and the nonlinear part  satisfies the  -Lipschitz condition with  belonging to an admissible function space. We prove the existence  of a (stochastic) inertial manifold for the solutions to the above equation.  Our method relies on the Lyapunov-Perron equation in a combination with the admissibility of function spaces. An application to the non-autonomous Chafee - Infante equations is given to illustrate our results.