学术报告

报告题目：Strong $(L^2,L^\gamma\cap H_0^1)$-continuity of reaction-diffusion equation in any space dimension

报告人：崔洪勇 博士（华中科技大学）

报告时间：2018年6月9日上午10:30-11:00

报告地点：25教14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，博士，华中科技大学数学与统计学院副研究员。2016年12月于西南大学获理学博士学位，2017年7月于西班牙塞维利亚大学（Universidad de Sevilla）获理学博士学位。主要研究领域是非自治与随机动力系统的渐近理论及应用，特别是吸引子的正则性、可测性以及对无穷维发展方程的渐近形态的刻画课题，其主要研究成果发表在J. Diff. Equs、J. Dyn. Diff. Equs、Nonl. Anal.等权威数学期刊上。