带有结构阻尼的半线性σ-发展方程解的整体存在唯一性  

The global existence and uniqueness of solutions of semi-linearσ -evolution equations with structural damping

作　　者：谢婷 杨晗[1] XIE Ting;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu,Sichuan 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《内江师范学院学报》2024年第12期16-21,共6页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11701477,11971394)。

摘　　要：研究带有结构阻尼的半线性σ-发展方程的Cauchy问题,利用Fourier分析法建立相应线性问题解的((L m∩L 2)-L 2)和(L 2-L 2)估计,借助整体迭代法,在小初值假设下,当非线性项指数p和空间维数n满足一定条件时证明解的整体存在唯一性并且得到解的衰减估计.This paper studies the Cauchy problem of semi-linearσ-evolution equations with structural damping,and the L m∩L 2-L 2 and L 2-L 2 estimates of the solutions of the corresponding linear problems are established by Fourier analysis.Employing the global i terative method and assuming small initial data,when the nonlinear term exponent p and the spatial dimension n meet certain conditions,the global existence and uniqueness of the solutions are proved and the decay estimates are obtained.

关 键 词：结构阻尼 σ-发展方程 CAUCHY问题 整体存在性 衰减估计 

分 类 号：O175[理学—数学]