應(yīng)yl7703永利官網(wǎng)楊璐教授邀請，俄羅斯國立研究大學(xué)高等經(jīng)濟(jì)學(xué)院A.V. Romanov副教授將于2019年6月30日至7月6日訪問我校并作學(xué)術(shù)報告。

報告題目：On the limit dynamics of systems of nonlinear parabolic equations

時    間：2019年7月5日上午9: 20

地    點(diǎn)：蘭州大學(xué)齊云樓911報告廳

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副教授簡介

A.V. Romanov副教授是國際無窮維動力系統(tǒng)領(lǐng)域的活躍專家之一，現(xiàn)為國立研究大學(xué)高等經(jīng)濟(jì)學(xué)院副教授。A.V. Romanov副教授于1966-1971獲得莫斯科國立大學(xué)學(xué)士學(xué)位，1976年獲得沃羅涅日州立大學(xué)博士學(xué)位。

A.V. Romanov副教授在動力系統(tǒng)和遍歷論、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.等國際學(xué)術(shù)期刊上發(fā)表學(xué)術(shù)論文20余篇。

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蘭州大學(xué)萃英學(xué)院

2019年7月3日