具有初值间断的Burgers方程奇摄动解

包立平; 胡玉博; 吴立群

doi:10.21656/1000-0887.400270

具有初值间断的Burgers方程奇摄动解

doi: 10.21656/1000-0887.400270

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

基金项目: 国家自然科学基金(51775154)；浙江省重点自然科学基金(LZ15E050004)

详细信息

作者简介:
包立平(1962—)，男，副教授，博士(E-mail: baolp@hdu.edu.cn)；胡玉博(1992—)，女，硕士生(通讯作者. E-mail: 1195595626@qq.com).

中图分类号: O175.29
计量
- 文章访问数: 1285
- HTML全文浏览量: 256
- PDF下载量: 296
- 被引次数: 0
出版历程
- 收稿日期: 2019-09-12
- 修回日期: 2019-11-04
- 刊出日期: 2020-07-01

Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P.R.China;²School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China(51775154)

摘要

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.
- Burgers方程 /
- 间断初值 /
- 特征线 /
- 奇摄动 /
- 一致有效性估计
Abstract: 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.
- Burgers equation /
- discontinuous initial value /
- characteristic line /
- singular perturbation /
- uniform validity estimation

HTML全文

参考文献(16)

[1]	SEN A, RAJA SEKHAR T. Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws[J]. Journal of Mathematical Physics,2019,60(5): 051510.
[2]	GALAKTIONOV V A. On self-similar collapse of discontinuous data for thin film equations with doubly degenerate mobility[R/OL]. 2009. [2019-09-12]. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.243.8638& rep=rep1& type=pdf.
[3]	瞿霞. 流体力学中Euler方程组的Riemann问题[D]. 硕士学位论文. 上海: 上海师范大学, 2019.(QU Xia. Riemann problem of Euler equations in fluid mechanics[D]. Master Thesis. Shanghai: Shanghai Normal University, 2019.(in Chinese))
[4]	SHEN C. The Riemann problem for the pressureless Euler system with the Coulomb-like friction term[J]. IMA Journal of Applied Mathematics,2015,81(1): 76-99.
[5]	WANG L. The Riemann problem with delta data for zero-pressure gas dynamics[J]. Chinese Annals of Mathematics(Series B),2016,37(3): 441-450.
[6]	ZHANG Y H, PAN R H, TAN Z. Zero dissipation limit to a Riemann solution consisting of two shock waves for the 1D compressible isentropic Navier-Stokes equations[J]. Science China: Mathematics,2013,56(11): 2205-2232.
[7]	HUANG F, WANG Y, YANG T. Vanishing viscosity limit of the compressible Navier-Stokes equations for solutions to a Riemann problem[J]. Archive for Rational Mechanics and Analysis,2012,203(2): 379-413.
[8]	CHEN Z, XIONG L, MENG Y J. Convergence to the superposition of rarefaction waves and contact discontinuity for the 1-D compressible Navier-Stokes-Korteweg system[J]. Journal of Mathematical Analysis and Applications,2014,412(2): 646-663.
[9]	CHEN Z Z, CHAI X J, WANG W J. Convergence rate of solutions to strong contact discontinuity for the one-dimensional compressible radiation hydrodynamics model[J]. Acta Mathematica Scientia,2016,〖STHZ〗 36(1): 265-282.
[10]	YOSHIA Z. Singular perturbation and scale hierarchy in plasma flows[C]// Autumn College on Plasma Physics: Long-Lived Structures and Self Organization in Plasmas . Trieste, Italy, 2003.
[11]	FERDOUSI M, YASMIN S, ASHRAF S, et al. Cylindrical and spherical ion-acoustic shock waves in nonextensive electron-positron-ion plasma[J]. IEEE Transactions on Plasma Science,2015,43(2): 643-649.
[12]	YANG X J, GAO F, SRIVASTAVA H M. Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations[J]. Computers & Mathematics With Applications,2017,73(2): 203-210.
[13]	SEADAWY A R. Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equation in quantum plasma[J]. Mathematical Methods in the Applied Sciences,2017,40(5): 1598-1607.
[14]	FANG B, TANG P, WANG Y G. The Riemann problem of the Burgers equation with a discontinuous source term[J]. Journal of Mathematical Analysis and Applications,2012,395(1): 307-335.
[15]	拉奥 C S, 亚达夫 M K. 非齐次Burgers方程解的渐近性行为[J]. 应用数学和力学, 2010,31(9): 1133-1139. (RAO C S, YADAV M K. Asymptotic behavior of solutions to nonhomogeneous Burgers equation[J]. Applied Mathematics and Mechanics,2010,31(9): 1133-1139.(in Chinese))
[16]	伍卓群, 尹景学, 王春明. 椭圆与抛物型方程引论[M]. 北京: 科学出版社, 2003.(WU Zhuoqun, YIN Jingxue, WANG Chunming. Introduction to Elliptic and Parabolic Equations [M]. Beijing: Science Press, 2003.(in Chinese))

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1285
HTML全文浏览量: 256
PDF下载量: 296
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

具有初值间断的Burgers方程奇摄动解

doi: 10.21656/1000-0887.400270

作者简介:
包立平(1962—)，男，副教授，博士(E-mail: baolp@hdu.edu.cn)；胡玉博(1992—)，女，硕士生(通讯作者. E-mail: 1195595626@qq.com).

计量

Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities

计量

目录

留言板

具有初值间断的Burgers方程奇摄动解

doi: 10.21656/1000-0887.400270

作者简介: 包立平(1962—)，男，副教授，博士(E-mail: baolp@hdu.edu.cn)；胡玉博(1992—)，女，硕士生(通讯作者. E-mail: 1195595626@qq.com).

计量

出版历程

Singularly Perturbed Solutions of Burgers Equations With Initial Value Discontinuities

计量

出版历程

目录

作者简介:
包立平(1962—)，男，副教授，博士(E-mail: baolp@hdu.edu.cn)；胡玉博(1992—)，女，硕士生(通讯作者. E-mail: 1195595626@qq.com).