三维热方程的profile分解  

Profile decomposition of three-dimensional heat equation

作　　者：韩依洋 程星 HAN Yiyang;CHENG Xing(College of Science,Hohai University,Nanjing 210000,China)

机构地区：[1]河海大学理学院,南京210000

出　　处：《黑龙江大学自然科学学报》2023年第4期379-382,共4页Journal of Natural Science of Heilongjiang University

基　　金：江苏省自然科学基金(BK20221497)。

摘　　要：研究了热方程的profile分解问题,主要思想是运用Sobolev不等式和Strichartz估计给出Sobolev嵌入的紧性缺失原因。并以一族正交profile分解和的形式证明在时空意义下余项是趋于零的。The profile decomposition problem of heat equation was studied.The main idea is to use Sobolev inequality and Strichartz estimation to provide the reason for the lack of compactness in Sobolev embedding.It was demonstrated in the form of a family of orthogonal profile decomposition sums that the remainder tends to zero in the spatiotemporal sense.

关 键 词：热方程 profile分解 STRICHARTZ估计 Sobolev嵌入 

分 类 号：O175.24[理学—数学]