Error estimation of wavelet regularization for solving oneside problem of two-dimensional heat equation
Yuan Li, Lixin Feng · Scientia Sinica Mathematica · 2011
We consider a two-dimensional sideways heat equation on R+2 , which is known to be an ill-posed problem. We propose a regularization approach by means of the orthogonal MRA generating the Meyer wavelet. The main reason for this is the fact that the Fourier transform of Meyer wavelet is known to be compactly supported. This means that they can be used to prevent high frequency noise from destroying the solution. The main result of the paper is Theorem 4.2 which is an error estimate of the exact solution with respect to a truncated one (i.e, wavelet regularized solution). The truncation is done by thresholding the measured data f and a level-wise discretization.