The regularization of non-autonomous non-linear ill-posed problems is established using a logarithmic approximation originally proposed by Boussetila and Rebbani, and later modified by Tuan and Trong. We first prove continuous dependence on modeling where the solution of the original ill-posed problem is estimated by the solution of an approximate well-posed problem. Finally, we illustrate the convergence via numerical experiments in spaces.
Submitted December 14, 2017. Published January 19, 2017.
Math Subject Classifications: 47D03, 35K91.
Key Words: Non-linear ill-posed problem; backward heat equation; non-autonomous problem; semigroup of linear operators; regularization.
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| Matthew Fury |
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