應(yīng)yl7703永利官網(wǎng)邀請，西班牙塞維利亞大學(xué) Tomás Caraballo 教授將于2023年6月13日舉辦學(xué)術(shù)報告。

報告題目：A survey on the dynamics of stochastic PDEs

時間：2023年6月13日(星期二)上午9:00

地點：城關(guān)校區(qū)理工樓631報告廳

報告摘要：The aim of this talk is to provide a survey on different aspects related to the dynamics of systems modeled by stochastic partial differential equations. We first report on the dynamics of random dynamical systems generated by stochastic PDE with linear multiplicative or additive noise. The main technique is a conjugation transformation which allows us to obtain a random dynamical system generated by the original stochastic problem. However, when the noise is more general than additive or multiplicative, this transformation does not work, but we still have two other alternatives to handle our problem. The first one consists in approximating the noisy term by a Wong-Zakai approximation (also called colored noise). In this way we can consider a random partial differential equation which generates a random dynamical system and the theory of random dynamical systems can be applied. A reason justifying this approach is that the random dynamical system generated by the Wong-Zakai approximation converges to the random dynamical system generated by the stochastic problem when the noise is additive or multiplicative. However, the convergence for general multiplicative noise is still unsolved. The second approach to analyze the case of nonlinear multiplicative noise is to apply the theory of weak mean random attractor which provides interesting information about the dynamics of the problem in an appropriate phase space.

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報告人簡介

Tomás Caraballo，西班牙塞維利亞大學(xué)終身教授，博士生導(dǎo)師，美國奧本大學(xué)客座教授，主要研究隨機(jī)偏微分方程吸引子的存在性和內(nèi)部結(jié)構(gòu)，隨機(jī)動力系統(tǒng)等。先后在SIAM J. Math. Anal.，J. Differential Equations，Proc. A，J. Dynam. Differential Equations，Nonlinear Anal.，Discrete Contin. Dynam. Systems等數(shù)學(xué)權(quán)威期刊上發(fā)表論文三百三十余篇，并著有《Applied Nonautonomous and Random Dynamical Systems, Applied Dynamical Systems》，多次受邀在華南理工大學(xué)，東華大學(xué)，華中科技大學(xué)等訪問并做報告。

甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級重點實驗室

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2023年6月8日