應(yīng)yl7703永利官網(wǎng)王智誠(chéng)教授的邀請(qǐng)，上海師范大學(xué)王榮年教授將于2021年11月27日-11月28日與我校有關(guān)師生進(jìn)行在線學(xué)術(shù)研討，其中11月27日舉行線上專(zhuān)題學(xué)術(shù)報(bào)告。

報(bào)告題目: Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications

時(shí)    間：11月27日10:00

地    點(diǎn)：騰訊會(huì)議ID：557250 177

摘 要：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.

歡迎廣大師生光臨!

王榮年教授簡(jiǎn)介

王榮年, 博士, 上海師范大學(xué)教授, 博士生導(dǎo)師（應(yīng)用數(shù)學(xué)）。目前主要從事非線性發(fā)展方程適定性、多值擾動(dòng)及解集的拓?fù)湔齽t性、不變流形理論等問(wèn)題的研究, 完成的研究結(jié)果已被"Mathematische Annalen"、“Int. Math. Res. Notices 、"Journal of Functional Analysis"、"Journal of Differential Equations"" Journal of Phys. A: Math. Theo."等學(xué)術(shù)期刊發(fā)表. 主持承擔(dān)了2項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目、國(guó)家自然科學(xué)基金青年項(xiàng)目、4項(xiàng)省自然科學(xué)基金項(xiàng)目和2項(xiàng)省教育廳基金項(xiàng)目。

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yl7703永利官網(wǎng)

萃英學(xué)院

2021年11月25日