确定表面热流的非标准逆热传导问题的Fourier正则化方法

Fourier Regularization Method for Determining Surface Heat Flux of Non-standard Inverse Conduction Problem

考虑确定热流ux(x ,t) ,0 ≤x<1的如下非标准逆热传导问题ut+ux =uxx 0 ≤x≤∞ ,0 <t <∞u(1,t) =g(t) 0≤t<∞u(x,0 ) =0 x≥ 0这是一个严重不适定问题 ,至今结果很少。文中给出了一种在频域的截断正则化方法 ,恢复了解对数据的连续依赖性 ,并给出了误差估计。

This paper tries to determine heat flux u_x(x,t), 0≤x<1, for the following non_standard inverse heat conduction problem: u_t+u_x=u_ xx 0≤x<∞,0<t<∞ u(1,t)=g(t) 0≤t<∞ u(x,0)=0x≥0 which is a seriously ill_posed problem, with few results obtained. A cur_off regularization method in the phase space is presented, and the continuous dependence of the solution upon the boundary data is recovered. The error estimation is also given.