Regularization of an Ill-Posed Hyperbolic Problem and the Uniqueness of the Solution by a Wavelet Galerkin Method
Year: 2012
Author: José Roberto Linhares de Mattos, Ernesto Prado Lopes
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 125–134
Abstract
We consider the problem K(x)uxx=utt, 0<x<1, t≥0, with the boundary condition u(0,t)=g(t)∈L2(R) and ux(0,t)=0, where K(x) is continuous and 0<α≤K(x)<+∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u(x,⋅)∈H2(R) and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore, we prove the uniqueness of the solution for this problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.3969/j.issn.1672-4070.2012.02.003
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 125–134
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: ill-posed problem meyer wavelet hyperbolic equation regularization.
Author Details
José Roberto Linhares de Mattos Email
Ernesto Prado Lopes Email