Article ID Journal Published Year Pages File Type
841336 Nonlinear Analysis: Theory, Methods & Applications 2010 11 Pages PDF
Abstract

Consider a nonlinear backward parabolic problem in the form ut+Au(t)=f(t,u(t)),u(T)=g, where AA is a positive self-adjoint unbounded operator. Based on the fundamental solution to the parabolic equation, we propose to solve this problem by the Fourier truncated method, which generates a well-posed integral equation. Then the well-posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one are proven. Our regularizing scheme can be considered a new regularization, with the advantage of a relatively small amount of computation compared with the quasi-reversibility or quasi-boundary value regularizations. Error estimates for this method are provided together with a selection rule for the regularization parameter. These errors show that our method works effectively.

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