一类非线性波动方程整体解的衰减估计  

The Decay Estimates of Global Solution for a Class of Nonlinear Wave Equation

作　　者：李梅玲 王云青 LI Mei-ling;WANG Yun-qing(Bohai Polytechnic Vocational College,Cangzhou 061199,China)

机构地区：[1]渤海理工职业学院基础部,河北沧州061199

出　　处：《数学的实践与认识》2020年第3期251-256,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11171311).

摘　　要：主要研究一类带有色散项和耗散项的高维非线性波动方程的柯西问题及衰减行为,利用双值分解和Bessel函数的一些性质给出其相应线性方程解的衰减估计,通过压缩映射原理证明了小初值条件下整体解的存在性和衰减估计.The Cauchy problem and asymptotic estimates for n dimension nonlinear wave equation with dissipation and dispersion term is investigated in this paper.The decay estimates of solution to the corresponding linear equation are given by using dyadic decomposition and some properties of Bessel functions.By the contraction mapping principle,we proved the global existence and asymptotic of the small amplitude solution.

关 键 词：波动方程 柯西问题 整体存在性 衰减估计 

分 类 号：O175[理学—数学]