数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 245-257.

• 论文 • 上一篇    下一篇

再生核空间中求解带有积分边界条件的半线性热传导方程

杜娟, 崔明根   

  1. 1.哈尔滨工业大学 数学系 山东威海 264209|2.哈尔滨师范大学 数学科学学院 哈尔滨 150025
  • 收稿日期:2008-07-23 修回日期:2009-10-14 出版日期:2010-01-01 发布日期:2010-01-01
  • 基金资助:

    黑龙江省自然科学基金(A2007-11)和黑龙江省教育厅科学技术研究项目(11541098)资助

Solving the Semilinear Heat Equation with Integral Boundary Conditions in the Reproducing Kernel Space

DU Juan, CUI Ming-Gen   

  1. 1.Department of Mathematics, Harbin Institute of Technology, Shandong Weihai 264209|2.School of Mathematics and Sciences, Harbin Normal University, Harbin 150025
  • Received:2008-07-23 Revised:2009-10-14 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    黑龙江省自然科学基金(A2007-11)和黑龙江省教育厅科学技术研究项目(11541098)资助

摘要:

该文给出了一个新的方法来求解带有积分边界条件的半线性热传导方程. 方程的精确解以级数的形式在再生核空间中给出. 证明了精确解的$n$项逼近是收敛于精确解的. 同时给出了一些算例说明了这个方法的有效性.

关键词: 半线性热传导方程, 积分边界条件, 再生核空间

Abstract:

In this paper, we give a new method to solve the semilinear heat equation with integral boundary conditions. Its
exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation un(x, t) of the exact solution u(x, t) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of
the present method.

Key words: Semilinear heat equation, Integral boundary condition, Reproducing kernel space

中图分类号: 

  • 34K10