Matthew Fury
Abstract:
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 Division of Science & Engineering Penn State Abington 1600 Woodland Road, Abington, PA 19001, USA email: maf44@psu.edu Tel 215-881-7553, Fax 215-881-7333 |
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