具有初值间断的Burgers方程奇摄动解  

Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities

作　　者：包立平[1] 胡玉博 吴立群[2] BAO Liping;HU Yubo;WU Liqun(School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,P.R.China;School of Mechanical Engineering,Hangzhou Dianzi University,Hangzhou 310018,P.R.China)

机构地区：[1]杭州电子科技大学理学院,杭州310018 [2]杭州电子科技大学机械工程学院,杭州310018

出　　处：《应用数学和力学》2020年第7期807-816,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51775154);浙江省重点自然科学基金(LZ15E050004)。

摘　　要：讨论激光等离子体产生的波模型,形成了具有初值间断的Burgers方程Riemann问题,通过奇摄动展开的方法得到了具有间断初值的Burgers方程相应形式的奇摄动渐近解,渐近解包含外解和内部层矫正两部分.由于初值条件是常数,波在传播的过程中产生特征边界,矫正项为抛物边界即抛物型特征边界.对外解在特征边界上进行内部层矫正,利用Hopf-Cole变换、Fourier变换、极值原理证明了渐近解的存在性、唯一性,得到了形式渐近展开式.证明了形式渐近解的一致有效性.The wave model generated for laser plasma was discussed, which can be expressed as the Riemann problem of Burgers equations with initial value discontinuity. The singularly perturbed asymptotic solution of the Burgers equations with discontinuous initial values was obtained with the singularly perturbed expansion method. The solution was divided into 2 parts: an outer solution and an inner layer correction term. Since the initial condition is constant, the wave will generate the characteristic boundary in the process of propagation, and the correction term will make the parabolic characteristic boundary. The external solution was corrected at the internal layer along the characteristic lines. The existence and uniqueness of the asymptotic solution was proved through the Hopf-Cole transform, Fourier transform and the extremum principle. Then the asymptotic expansion is obtained with the uniform validity proved.

关 键 词：BURGERS方程 间断初值 特征线 奇摄动 一致有效性估计 

分 类 号：O175.29[理学—数学]