关键词: 逆热传导问题, 不适定问题, 正则化, 误差估计, Meyer小波

Abstract:

We consider the non-standard inverse heat conduction problem of determiniting  the heat flux u_x(x, t), 0<x<1 from a measured temperature at x=1
u_t+u_x=u_xx,      x>0, t>0,

u(1, t)=g(t), t ≥0,

u(x, 0)=0, x≥0,

u(x, t)|_x→∞, bounded.
This problem is severely ill-posed.  In this paper, we analyse the problem ill-posedness, give a wavelet regularization solution based on an application of Meyer wavelet.  And  error estimate with H\"{o}lder type between the exact solution and the regularized solution is given at

(√2-√π/3)/√2<x<1.  The numerical experiment result shows that the regularization solution may converge to the exact solution for 0<x<1.

Key words: Inverse heat conduction problem, Ill-posed problem, Regularization, Error estimate, Meyer wavelet