再生核空间中的求解热传导方程反问题

Solving inverse problem for heat conduction equation in reproducing kernel space

在再生核空间中讨论了一类热传导方程反问题的求解方法,利用未知参数p(t)将解w(t,x)的表达式以级数的形式精确的表达出来,再联立附加条件即可同时解出未知参数p(t)和解w(t,x),最后以数值算例来说明此方法的简单可行性。

In this paper, the method for solving the inverse problem for a heat conduction equation in the reproducing kernel space is discussed. Employing unknown parameter p（t）, the solution w （t, x） is exactly represented in the form of series. And considering additional condition, both the unknown parameter p（t） and the solution w（ t, x） can be obtained. The solution of numerical example proves the method as simple and feasible.