数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1112-1121.

• 论文 • 上一篇    下一篇

多维空间一般Benjamin-Bona-Mahony 方程解的逐点估计

徐红梅|许盈盈   

  1. 河海大学理学院 南京 |210098
  • 收稿日期:2012-09-12 修回日期:2013-06-03 出版日期:2013-12-25 发布日期:2013-12-25
  • 基金资助:

    国家自然科学基金(11101121)资助

Pointwise Estimates of Solutions of Generalized Benjamin-Bona-Mahony Equations in Multi Dimensions

 XU Hong-Mei, XU Ying-Ying   

  1. College of Science, Hohai University, Nanjing 210098
  • Received:2012-09-12 Revised:2013-06-03 Online:2013-12-25 Published:2013-12-25
  • Supported by:

    国家自然科学基金(11101121)资助

摘要:

研究多维空间一般 Benjamin-Bona-Mahony 方程解的逐点估计. 通过傅里叶变换、拟微分算子、微局部分析,可以得到这个方程解的逐点收敛估计.  由于衰减速度和热传导方程相同,因此得到的衰减估计是最优的.

关键词: 柯西问题, 一般Benjamin-Bona-Mahony方程, 多维空间, 逐点估计

Abstract:

We study the pointwise estimates of the generalized Benjamin-Bona-Mahony equations in multi dimensional space. By using Fourier analysis, pseudo-differential operators and microlocal analysis, we obtain the pointwise convergence rates of the solution. The decay rate is optimal since it is as same as for the heat equation.

Key words: Cauchy problem, Generalized Benjamin-Bona-Mahony equation, Multi , dimensions, Pointwise estimate

中图分类号: 

  • 35G25