Electron. J. Differential Equations, Vol. 2018 (2018), No. 28, pp. 1-11.

Logarithmic regularization of non-autonomous non-linear ill-posed problems in Hilbert spaces

Matthew Fury

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 $L^2$ 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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