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数学进展 - 2018, Vol. 47(2): 224-230
研究论文
闭流形上热方程的$L^{1}$和$L^{2}$能量
$L^{1}$} and $L^{2}$ Energy for Heat Equations on Closed Manifolds

曾凡奇1,黄广月2
ZENG Fanqi1,*, HUANG Guangyue2}}

1. 同济大学数学科学学院, 上海, 200092;
2. 河南师范大学数学与信息科学学院, 新乡, 河南, 453007
1. School of Mathematical Sciences, Tongji University, Shanghai, 200092, P. R. China;
2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, P. R. China

收稿日期: 2016-07-08
出版日期: 2018-05-16
2018, Vol. 47(2): 224-230
DOI: 10.11845/sxjz.2016089b


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摘要 本文研究了具有加权测度的闭Riemann 流形上非线性热方程的$L^{1}$ 和 $L^{2}$能量的 衰减速度. 我们的结果可以看作是文献[Acta Math. Sin., Engl. Ser., 2014, 30(10): 1729-1734]的结果的一个推广.
关键词 加权拉普拉斯单调性非线性热方程闭黎曼流形    
Abstract:The purpose of this paper is to study the decay rates of $L^{1}$ and $L^{2}$ energy for the nonlinear heat equations on closed Riemannian manifolds with weighted measure. Our results can be seen as an extention of the work of Ma in [Acta Math. Sin., Engl. Ser., 2014, 30(10): 1729-1734].
Key wordsdrifting Laplacian    monotonicity    nonlinear heat equation    closed Riemannian manifold
PACS:  O186.12  
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