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A quasi-boundary value method for regularizing nonlinear ill-posed problems. (English) Zbl 1178.35374
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 1246.35104); Electron. J. Differ. Equ. 2008, Paper No. 33, 14 p., electronic only (2008; Zbl 1171.35488)] and by G. W. Clark and S. F. Oppenheimer [Electron. J. Differ. Equ. 1994/08 (1994; Zbl 0811.35157)].
MSC:
35R25Improperly posed problems for PDE
35M30Systems of mixed type
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M15Error bounds (IVP of PDE)