带有变系数阻尼项的半线性波动方程解的衰减估计  

Decay estimates of solutions for semilinear wave equations with variable coefficient damping terms

作　　者：陈雪丽 曹德刚 杨晗[1] CHEN Xue-li;CAO De-gang;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《西南民族大学学报（自然科学版）》2023年第3期328-333,共6页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11701477,11971394)。

摘　　要：研究一类在全空间■上带有变系数阻尼项的半线性波动方程的Cauchy问题,考虑阻尼项中的变系数是只与时间相关的函数,同时考虑非线性项为|u|^(p-1 )u的情形.假设变系数满足一定条件使得研究问题中的阻尼项是有效的,并且假设初值具有紧支集,利用乘子法以及解的有限传播速度性质来研究解的衰减性质,通过选取具体的乘子,得到了问题解的衰减估计.The purpose of this paper is to study the Cauchy problem of a class of semilinear wave equations with variable coefficient damping term in R^(n),considering the problem for the wave equation with time-dependent dissipation and a power nonlinearity|u|^(p-1 )u.Supposing that the damping term in the problem is effective if the variable coefficient meets certain conditions and that the initial data have a compact support,the decay property of the solution is studied by using the multiplier method and the finite propagation speed property of the solution.By selecting specific multipliers,the decay estimates of the solution are obtained.

关 键 词：变系数半线性波动方程 CAUCHY问题 乘子法 衰减估计 

分 类 号：O175.2[理学—数学]