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Abstract by Junyilang Zhao

Personal Infomation


Presenter's Name

Junyilang Zhao

Co-Presenters

None

Degree Level

Doctorate

Co-Authors

None

Abstract Infomation


Department

Mathematics

Faculty Advisor

Kening Lu

Title

Invariant Manifolds and Foliations for a Random Differential Equation

Abstract

We consider the random differential equation, du/dt=Au+f(u)+g(u) (W(t+delta)-W(t))/delta, which is an approximation for a stochastic differential equation with the same structure. Here W is a Hilbert space valued Wiener process. We show that under certain hypotheses on A, f, and g, there exist local invariant manifolds and foliations for this system, which are indeed given by smooth local graphs. Further applications are to be suggested as well.