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Zbl 1178.35374
Trong, Dang Duc; Quan, Pham Hoang; Tuan, Nguyen Huy
A quasi-boundary value method for regularizing nonlinear ill-posed problems. (English)
[J] Electron. J. Differ. Equ. 2009, Paper No. 109, 16 p., electronic only (2009). ISSN 1072-6691/e

Summary: 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 [Z. Anal. Anwend. 26, No. 2, 231--245 (2007; Zbl 05202594); Electron. J. Differ. Equ. 2008, Paper No. 33, 14 p., electronic only (2008; Zbl 1171.35488)] and by {\it G. W. Clark} and {\it S. F. Oppenheimer} [Electron. J. Differ. Equ. 1994/08 (1994; Zbl 0811.35157)].

MSC 2000:: *35R25 Improperly posed problems for PDE
35M30
65M60 Finite numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)

Keywords: backward heat problem; nonlinearly ill-posed problem; quasi-boundary value methods; quasi-reversibility methods; contraction principle

Citations: Zbl 1171.35488; Zbl 0811.35157; Zbl 05202594

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