应best365在线官网登录入口杨璐教授邀请，俄罗斯国立研究大学高等经济学院A.V. Romanov副教授将于2019年6月30日至7月6日访问我校并作学术报告。

报告题目：On the limit dynamics of systems of nonlinear parabolic equations

时    间：2019年7月5日上午9: 20

地    点：beat365正版唯一齐云楼911报告厅

摘    要：We are considering the question of the finite dimensionality of the dynamics on the global attractor (FDA property) for dissipative spatially inhomogeneous systems of equations of the form

ut = uxx + f(x, u, ux), x∈(0, 1), (1)

with u = (u1,・・・, um) and C3- function f = f(x, u, p) under boundary conditions (D), (N) or (P) and the appropriate choosing the phase Hilbert space H. We install (on the basis of the method) FDA property under the Dirichlet and Neumann conditions for nonlinearity f of a general form, and in the periodic case with provided that the matrix function fp on the attractor A⊂H is diagonal.

We trace links with the works, in which spatially homogeneous systems (1) with f = f(u, ux) were considered from the point view of the presence of a smooth inertial manifold (IM) - properties stronger than FDA. The existence of IM is proved for problems (1)-(D) and (1)-(N). For more delicate the periodic case, the existence of IM is established with provided that the matrix fp is diagonal with a unique nonzero element.

A.V. Romanov副教授简介

A.V. Romanov副教授是国际无穷维动力系统领域的活跃专家之一，现为国立研究大学高等经济学院副教授。A.V. Romanov副教授于1966-1971获得莫斯科国立大学学士学位，1976年获得沃罗涅日州立大学博士学位。

A.V. Romanov副教授在动力系统和遍历论、偏微分方程等方面做出了杰出的工作。先后在Dyn. Partial Differ. Equ.、Ergodic Theory Dynam. Systems、Math. Notes、Funct. Anal. Appl.等国际学术期刊上发表学术论文20余篇。

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2019年7月3日