带调和振荡算子的非线性热方程的Gelfand-Shilov光滑性效应  

Gelfand-Shilov Smoothing Effect for Nonlinear Heat Equation Associated to Harmonic Oscillators

作　　者：田媛媛 李浩光 TIAN Yuanyuan;LI Haoguang(School of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,湖北武汉430074

出　　处：《应用数学》2024年第3期739-748,共10页Mathematica Applicata

基　　金：the Natural Science Foundation of Hubei province,China(2022CFB444)。

摘　　要：在本文中,我们证明在s>1/2的Shubin空间Qs(R)中带调和振荡算子的非线性热方程Cauchy问题解的整体存在性和Gelfand-Shilov光滑性效应.这是在已有工作的基础上对正则性的一个改进的新论证.In this work,we show the global existence and Gelfand-Shilov smoothing effect of the solution to the Cauchy problem of the nonlinear heat equation associated to Harmonic oscillators with the initial data in the Shubin class Q s(R)where s>1/2.We give an improved new argument in the regularity property on the basis of the work[3].

关 键 词：非线性热方程 整体存在性 Gelfand-Shilov光滑性效应 调和振荡算子 Shubin空间 

分 类 号：O175.26[理学—数学]