具有间断初值波方程Riemann问题奇摄动解  

Singularly Perturbed Solutions of Riemann Problem for Wave Equations with Discontinuous Initial Values

作　　者：胡玉博 包立平[1] HU Yubo;BAO Liping(Institute of mathematics,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学数学研究所

出　　处：《杭州电子科技大学学报（自然科学版）》2019年第6期94-99,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(51775154)

摘　　要：讨论了小振幅声波在弱阻尼介质中传播的问题,可用一类具有间断初值的线性混合型波方程来描述。通过奇摄动方法对具有间断初值的线性混合型波方程构造相应形式的渐近解,渐近解包含外解和内部层校正两部分。外解在影响区域边界产生角层现象,通过内部层校正,并进行余项估计得到L 2意义下渐近解的一致有效性、连续性和一阶导函数连续的结果,相比于无阻尼情形,提高了渐近解的正则性。The propagation of small amplitude acoustic waves in weakly damped media is discussed.It can be described by a class of linear mixed wave equations with discontinuous initial values.The asymptotic solutions of linear mixed wave equation with discontinuous initial values are constructed by singular perturbation methods.The asymptotic solution contains two parts of the outer solution and the inner layer correction.Outer solution produces angular phenomena at the boundary of the affected area.Corrected by internal layer,and the residual estimate is used to obtain the consistent validity result of the asymptotic solution in the L 2 sense.It can be obtained that the singularly perturbed solution is continuous,whose first-order derivative is also obtained.The results show that the regularity of the asymptotic solution is improved compared with the case without damp.

关 键 词：奇摄动 线性混合型波方程 RIEMANN问题 影响域 不连续 

分 类 号：O175.2[理学—数学]