Wavelet method for solving the unsteady porous-medium flow problem with discontinuous coefficients

A method is proposed for constructing stable approximate wavelet decompositions of weak solutions to boundary value problems for the unsteady porous-medium flow equation with discontinuous coefficients and inexact data. The method is based on the general scheme for finite-dimensional approximation in Tikhonov regularization and on multiresolution analysis with basis functions defined as the product of one-dimensional Daubechies wavelets.