Table of Contents
ISRN Mathematical Analysis
Volume 2014 (2014), Article ID 525636, 8 pages
http://dx.doi.org/10.1155/2014/525636
Research Article

A Regularization Method for the Elliptic Equation with Inhomogeneous Source

1Faculty of Mathematics-Statistics, Ton Duc Thang University, Nguyen Huu Tho Street, District 7, Ho Chi Minh City, Vietnam
2Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam

Received 31 July 2013; Accepted 3 October 2013; Published 4 March 2014

Academic Editors: F. Colombini and G. L. Karakostas

Copyright © 2014 Tuan H. Nguyen and Binh Thanh Tran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the following Cauchy problem for the elliptic equation with inhomogeneous source in a rectangular domain with Dirichlet boundary conditions at and . The problem is ill-posed. The main aim of this paper is to introduce a regularization method and use it to solve the problem. Some sharp error estimates between the exact solution and its regularization approximation are given and a numerical example shows that the method works effectively.