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.
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Phát hành ngày
2019-10-28
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