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Southwest Jiaotong University School of Mathematics

数学系

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

澳门金莎娱乐网站:   编辑:黎定仕     日期:2018-06-12 08:57:40   点击数:  

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

时间:6月13日(星期三)     下午   4:00-4:50

地点:X2511

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 Peter Kloeden and Wenqiang Zhao.



报告人概况:崔洪勇,博士,华中科技大学数学与统计学院博士后。201612月于西南大学获理学博士学位,20177月于西班牙塞维利亚大学(Universidad de Sevilla)获数学博士学位。主要研究领域是非自治与随机动力系统,其主要研究成果发表在 J. Diff. EqusJ. Dyn. Diff. EqusPhysica D等专业期刊上。


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