THE SPARSE REPRESENTATION RELATED WITH FRACTIONAL HEAT EQUATIONS  

作　　者：曲伟 钱涛 梁应德 李澎涛 Wei QU;Tao QIAN;Ieng Tak LEONG;Pengtao LI(College of Sciences,China Jiliang University,Hangzhou,310018,China;Macao Center for Mathematical Science,Macao University of Science and Technology,Macao,999078,China;Department of Mathematics,Faculty of Science and Technology,University of Macao,Macao,999078,China;School of Mathematics and Statistics,Qingdao University,Qingdao,266071,China)

机构地区：[1]College of Sciences,China Jiliang University,Hangzhou,310018,China [2]Macao Center for Mathematical Science,Macao University of Science and Technology,Macao,999078,China [3]Department of Mathematics,Faculty of Science and Technology,University of Macao,Macao,999078,China [4]School of Mathematics and Statistics,Qingdao University,Qingdao,266071,China

出　　处：《Acta Mathematica Scientia》2024年第2期567-582,共16页数学物理学报（B辑英文版）

基　　金：supported by the Science and Technology Development Fund of Macao SAR(FDCT0128/2022/A,0020/2023/RIB1,0111/2023/AFJ,005/2022/ALC);the Shandong Natural Science Foundation of China(ZR2020MA004);the National Natural Science Foundation of China(12071272);the MYRG 2018-00168-FST;Zhejiang Provincial Natural Science Foundation of China(LQ23A010014).

摘　　要：This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.

关 键 词：reproducing kernel Hilbert space DICTIONARY sparse representation approximation to the identity fractional heat equations 

分 类 号：O177[理学—数学] O175.2[理学—基础数学]