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非齐次Burgers方程解的渐近性行为

C·S·拉奥 M·K·亚达夫

C·S·拉奥, M·K·亚达夫. 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. doi: 10.3879/j.issn.1000-0887.2010.09.012
引用本文: C·S·拉奥, M·K·亚达夫. 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. doi: 10.3879/j.issn.1000-0887.2010.09.012
Ch. Srinivasa Rao, Manoj K Yadav. Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1133-1139. doi: 10.3879/j.issn.1000-0887.2010.09.012
Citation: Ch. Srinivasa Rao, Manoj K Yadav. Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1133-1139. doi: 10.3879/j.issn.1000-0887.2010.09.012

非齐次Burgers方程解的渐近性行为

doi: 10.3879/j.issn.1000-0887.2010.09.012
基金项目: 印度科学和工业研究委员会资助项目(09/84(366)/2005-EMR-I)
详细信息
  • 中图分类号: O175.24

Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation

  • 摘要: 构造了非齐次Burgers方程的解,方程服从有界和紧致的初始曲线,作了一个有趣的探索.将热方程初值问题(L2(R,ex2/2)中有初值)的解,表示为该热方程自相似解的一个级数,Kloosterziel方法立即显示出该初值问题解的渐近性行为.受Kloosterziel方法的启发,根据热方程的自相似解,来表示非齐次Burgers方程的解.最后得到该非齐次Burgers方程解的渐近性特征.
  • [1] Ablowitz M J, De Lillo S. The Burgers equation under deterministic and stochastic forcing [J]. Physica D, 1996, 92(3/4):245-259. doi: 10.1016/0167-2789(95)00274-X
    [2] Balogh A, Gilliam D S, Shubov V I. Stationary solutions for a boundary controlled Burgers’equation [J]. Math Comput Model, 2001, 33(1/3): 21-37. doi: 10.1016/S0895-7177(00)00226-0
    [3] Gao Y T, Xu X G, Tian B. Variable-coefficient forced Burgers system in nonlinear fluid mechanics and its possibly observable effects[J]. Int J Mod Phys C, 2003, 14(9): 1207-1222. doi: 10.1142/S0129183103005340
    [4] Gurarie V, Migdal A. Instantons in the Burgers equation[J]. Phys Rev E, 1996, 54(5):4908-4914. doi: 10.1103/PhysRevE.54.4908
    [5] Xu T, Zhang C-Y, Li J, Meng X-H, Zhu H-W, Tian B. Symbolic computation on generalized Hopf-Cole transformation for a forced Burgers model with variable coefficients from fluid dynamics[J]. Wave Motion, 2007, 44(4): 262-270. doi: 10.1016/j.wavemoti.2006.10.004
    [6] Kloosterziel R C. On the large-time asymptotics of the diffusion equation on infinite domains[J]. J Engrg Math, 1990, 24(3): 213-236. doi: 10.1007/BF00058467
    [7] Higgins J R. Completeness and Basic Properties of Sets of Special Functions[M]. Cambridge:Cambridge University Press, 1977.
    [8] Ding X-Q, Jiu Q-S, He C. On a nonhomogeneous Burgers’equation[J]. Sci China Ser A, 2001, 44(8): 984-993. doi: 10.1007/BF02878974
    [9] Rao C S, Yadav M K. Solutions of a nonhomogeneous Burgers equation[J]. Stud Appl Math, 2010, 124(4): 411-422. doi: 10.1111/j.1467-9590.2009.00478.x
    [10] Polyanin A D. Handbook of Linear Partial Differential Equations for Engineers and Scientists[M].New York:Chapman & Hall/CRC, 2002.
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-06-04
  • 刊出日期:  2010-09-15

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