报告题目：A strong continuity result of reaction-diffusion equations via a decomposition of the  nonlinear term

报告人：崔洪勇（华中科技大学）

报告时间：2019年1月26日上午：10:00-11:00

报告地点：数学院三楼报告厅

报告摘要: 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.

报告人简介：崔洪勇，男，理学博士。分别于2016年12月和2017年7月获西南大学和塞维利亚大学（西班牙）双博士学位，2017年1月至2018年12月华中科技大学博士后。现华中科技大学数学与统计学院讲师，美国“数学评论”评论员。崔洪勇博士主要从事非自治和随机动力系统的吸引子理论研究，近几年以第一作者在J. Diff. Equ., J. Dyn. & Diff. Equ., Phys. D等专业期刊上发表研究论文15篇，主持国家自然科学基金青年项目1项，中国博士后科学基金面上项目1项。