Electron. J. Diff. Equ., Vol. 2009(2009), No. 109, pp. 1-16.

A quasi-boundary value method for regularizing nonlinear ill-posed problems

Dang Duc Trong, Pham Hoang Quan, Nguyen Huy Tuan

In this article, a modified quasi-boudary regularization method for solving nonlinear backward heat equation is given. Sharp error estimates for the approximate solutions, and numerical examples to illustrate the effectiveness our method are provided. This work extends to the nonlinear case earlier results by the authors [33,34] and by Clark and Oppenheimer [6].

Submitted June 19, 2009. Published September 10, 2009.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Backward heat problem; nonlinearly Ill-posed problem, quasi-boundary value methods; quasi-reversibility methods, contraction principle.

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Dang Duc Trong
Department of Mathematics and Informatics
Hochiminh City National University
227 Nguyen Van Cu, Q. 5, Hochiminh City, Vietnam
email: ddtrong@mathdep.hcmuns.edu.vn
Pham Hoang Quan
Department of Mathematics, Sai Gon University
273 An Duong Vuong, Ho Chi Minh city, Vietnam
email: tquan@pmail.vnn.vn
Nguyen Huy Tuan
Department of Information Technology and Mathematics
Ton Duc Thang University
98 Ngo Tat To, Hochiminh City, Vietnam
email: tuanhuy_bs@yahoo.com

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