Wavelets and regularization of the sideways heat equation

Abstract

In this paper, the following inverse heat conduction problem: u t = u xx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u| x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in H r( R)-norm meaning is given.