報告題目：A strong continuity result of reaction-diffusion equations via a decomposition of the  nonlinear term

報告人：崔洪勇（華中科技大學）

報告時間：2019年1月26日上午：10:00-11:00

報告地點：數學院三樓報告廳

報告摘要: In this talk we are concerned with the continuity in initial data of a classical reaction-diffusion equation with arbitrary $p>2$ order nonlinearity and in any space dimension $N\geq 1$. We shall show that, with the external forcing only in $ L^2$, the weak solutions can be strong $(L^2, L^\gamma\cap H_0^1)$-continuous for any $\gamma\geq 2$ (independent of the physical parameters of the system), i.e., can converge in the norm of any $L^\gamma\cap H_0^1$ as the corresponding initial values converge in $L^2$. The main technique we employ is a decomposition method of the nonlinearity, splitting the nonlinearity into two, one providing better properties which leads to the desired results and the other remaining controllable. Applying this to the global attractor we will obtain some new topological properties as well as a upper bound of the fractal dimension of the attractor in $L^\gamma\cap H_0^1$ by that in $L^2$. This is a joint work with Profs. Peter Kloeden and Wenqiang Zhao.

報告人簡介：崔洪勇，男，理學博士。分別于2016年12月和2017年7月獲西南大學和塞維利亞大學（西班牙）雙博士學位，2017年1月至2018年12月華中科技大學博士后。現華中科技大學數學與統計學院講師，美國“數學評論”評論員。崔洪勇博士主要從事非自治和隨機動力系統的吸引子理論研究，近幾年以第一作者在J. Diff. Equ., J. Dyn. & Diff. Equ., Phys. D等專業期刊上發表研究論文15篇，主持國家自然科學基金青年項目1項，中國博士后科學基金面上項目1項。