應(yīng)yl7703永利官網(wǎng)楊璐教授邀請,俄羅斯科學(xué)院信息傳輸問題研究所首席科學(xué)研究員VladimirChepyzhov將于2024年9月1日至9月6日訪問我校并作系列學(xué)術(shù)報告。
報告題目一：Dynamical semigroups and global attractors
時間：2024年9月2日（星期一）上午9: 30-10: 30
地點(diǎn)：大學(xué)生活動中心506報告廳
報告題目二：Global attractors：Application to evolution equations (ODEs and PDEs).
時間：2024年9月2日（星期一）上午10: 30-11: 30
地點(diǎn)：大學(xué)生活動中心506報告廳
報告題目三：Trajectory attractors for ODEs without uniqueness
時間：2024年9月3日（星期二）上午9: 30-10: 30
地點(diǎn)：大學(xué)生活動中心506報告廳
報告題目四：Theory of trajectory attractors and applications to PDEs (reaction-diffusion systems, 3D Navier-Stokes equations).
時間：2024年9月3日（星期二）上午10: 30-11: 30
地點(diǎn)：大學(xué)生活動中心506報告廳
報告摘要：These talks are devoted to the theory of trajectory attractors of dissipative partial differential equations (PDEs). Many important problems arising in mechanics and physics lead to the study of complicated evolution PDEs and especially to the study of their solutions as time tends to infinity. For the last 5 decades, the considerable progress in solving such problems has been achieved using the theory of infinite dimensional dynamical systems and their attractors. The classical approach suggests to consider the dynamical semigroup in the phase space of initial data of the PDE under the study, which is a Hilbert or Banach space. After that, one looks for a
global attractor of this semigroup. However, to construct such single-valued semigroup the involved Cauchy problem must be uniquely solvable on arbitrary long time interval. If the solution is not unique, or the uniqueness theorem is unknown, then the classical approach is not directly applicable. Recall, there are many important PDEs for which that is the case. For example, the famous 3D Navier-Stokes system is a bounded domain. To overcome this drawback of the classical theory, one can use the theory of so-called trajectory dynamical system and their trajectory attractors developed in the works of Mark Vishik and Vladimir Chepyzhov, presented in this mini-course. In two starting lectures we will shortly expose the classical approach with application to dissipative evolution equations (ODEs and PDEs), such as reaction-diffusion systems and 2D Navier-Stokes system. In lecture 3, we explain the method of trajectory dynamical systems using quite simple but substantial system of ODEs without uniqueness of their solutions. In lecture 4, we explain how this theory is applicable to more complicated reaction-diffusion systems and to inhomogeneous 3D Navier-Stokes system in a bounded domain, for which, as has been shown in the recent works, the long standing hypothesis of the uniqueness is closed to be refute. So, the trajectory attractors are very important in the study of long time behaviour for solutions of this and other PDEs without uniqueness.
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報告人簡介
V. Chepyzhov研究員（科學(xué)博士）作為無窮維動力系統(tǒng)蘇聯(lián)學(xué)派著名數(shù)學(xué)家M.Vishik教授的代表性學(xué)生之一，是國際上無窮維動力系統(tǒng)領(lǐng)域的杰出學(xué)者和新一代的代表學(xué)者之一?，F(xiàn)任俄羅斯科學(xué)院信息傳輸問題研究所首席科學(xué)研究員。主要從事無窮維動力系統(tǒng)吸引子理論的研究，特別是在一致吸引子和軌道吸引子的基礎(chǔ)理論方面做出了奠基性以及深刻創(chuàng)新的工作，與M. Vishik教授共同撰寫的專著是本領(lǐng)域的經(jīng)典著作之一，到目前發(fā)表學(xué)術(shù)論文95篇（數(shù)據(jù)來源于MathSciNet數(shù)據(jù)庫），被引用文獻(xiàn)次數(shù)達(dá)2198次。其中多篇論文都發(fā)表在Comm. Pure Appl. Math.，J. Math. Pures Appl.，Indiana Univ. Math. J.，Russian Math. Surveys等國際頂尖學(xué)術(shù)期刊上。
甘肅應(yīng)用數(shù)學(xué)中心
甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級重點(diǎn)實(shí)驗(yàn)室
yl7703永利官網(wǎng)
萃英學(xué)院
2024年8月27日
