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
재생핵공간중구해대유적분변계조건적반선성열전도방정
Solving the Semilinear Heat Equation with Integral Boundary Conditions in the Reproducing Kernel Space
  • 万方数据
    数学物理学报 수학물이학보
    ACTA MATHEMATICA SCIENTIA
    2010年 1期 245-257 ,共13页

    杜娟%崔明根

    두연%최명근

    半线性热传导方程%积分边界条件%再生核空间 半線性熱傳導方程%積分邊界條件%再生覈空間
    반선성열전도방정%적분변계조건%재생핵공간
    Semilinear heat equation%Integral boundary condition%Reproducing kernel space
    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.
    해문급출료일개신적방법래구해대유적분변계조건적반선성열전도방정.방정적정학해이급수적형식재재생핵공간중급출.증명료정학해적n항핍근시수렴우정학해적.동시급출료일사산례설명료저개방법적유효성.
    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 u_n(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.
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