Đang chuẩn bị liên kết để tải về tài liệu:
Non-autonomous stochastic evolution equations, inertial manifolds and Chafee-infante models

Consider a stochastic evolution equation containing Stratonovich-multiplicative white noise of the form ( , ) du Au f t u u W dt where the partial differential operator A is positive definite, self-adjoint with a discrete spectrum; and the nonlinear part f 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. |