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Regularization of an Ill-Posed Hyperbolic Problem and the Uniqueness of the Solution by a Wavelet Galerkin Method

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, t0, with the boundary condition u(0,t)=g(t)L2(R) and ux(0,t)=0, where K(x) is continuous and 0<αK(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