Invited by Prof. Zhicheng Wang of School of Mathematics and Statistics, Prof. Nongnian Wang from Shanghai Normal University will give lectures online.

Title：Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications

Time：10:00 a.m.,Nov. 27th, 2021

Conference ID：557250 177( Tencent Conference)

Abstract：We consider an abstract nonautonomous dynamical system defined on a general Banach space. We prove that if a geometrical assumption, called local strong squeezing property, and several technical assumptions, called controllability, inverse Lipschitz, and (partial) compactness property, are satisfied, then the system admits a finite-dimensional Lipschitz invariant manifold with an exponential tracking property acting on a local range. We then apply this general framework to two types of nonautonomous evolution equations: Reaction-diffusion equations and FitzHugh-Nagumo systems, driven by time-dependent additive/multiplicative forces, on a 2-D rectangular domain or a 3-D cubic domain. It issignificant that on the 3D domain the spectrum of the linear unbounded operator in the principal part does not have arbitrarily large gaps.We prove the existence of an inertial manifold of nonautonomous type for the former while a finite-dimensional global manifold for the latter. Each manifold controls the long-time behavior of solutions of the corresponding system.