In:
Asian-European Journal of Mathematics, World Scientific Pub Co Pte Ltd, Vol. 04, No. 01 ( 2011-03), p. 145-161
Abstract:
In this paper, we consider an inverse time problem for a nonlinear parabolic equation in the form u t + Au(t) = f(t, u(t)), u(T) = φ, where A is a positive self-adjoint unbounded operator and f is a Lipschitz function. As known, it is ill-posed. Using a quasi-reversibility method, we shall construct regularization solutions depended on a small parameter ϵ. We show that the regularized problem is well-posed and that their solution u ϵ (t) converges on [0, T] to the exact solution u(t). This paper extends the work by Dinh Nho Hao et al. [8] to nonlinear ill-posed problems. Some numerical tests illustrate that the proposed method is feasible and effective.
Type of Medium:
Online Resource
ISSN:
1793-5571
,
1793-7183
DOI:
10.1142/S1793557111000125
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2011
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