一类双阻尼σ-发展方程解的整体存在唯一性  

Existence and Uniqueness of Global Solutions for a Class of Double Dampedσ-evolution Equations

作　　者：刘梅 何鑫海 杨晗[1] 明森 Liu Mei;He Xinhai;Yang Han;Ming Sen(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;School of Science,North University of China,Taiyuan 038507,China)

机构地区：[1]西南交通大学数学学院,成都611756 [2]中北大学理学院,太原038507

出　　处：《数学理论与应用》2022年第4期1-18,共18页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(Nos.11701477,11971394)资助。

摘　　要：本文研究一类带有不同幂次非线性项的双阻尼σ-发展方程的柯西问题,利用Fourier变换建立相应线性问题解的(L^(m)∩L^(2))-L^(2)估计,进而利用整体迭代法在小初值情形研究非线性项指数对整体解的存在性的影响,并给出解整体存在时指数p应满足的条件.This paper studies the Cauchy problem for a class of double dampedσ-evolution equations with different power nonlinearities.The(L^(m)∩L^(2))-L^(2) estimates of solution to the corresponding linear problem is established by using the Fourier transform,and then the influence of the exponential of the nonlinear term on the existence of the global solution is studied by employing the global iterative method in the case of small initial value.Moreover,the conditions that the index p should satisfy for the existence of global solution are given.

关 键 词：双阻尼 σ-发展方程 柯西问题 整体迭代法 整体存在性 

分 类 号：O175[理学—数学]