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

Date
2018-01-19
Authors
Fury, Matthew
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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 L2 spaces.
Description
Keywords
Non-linear ill-posed problem, Backward heat equation, Non-autonomous problem, Semigroup of linear operators, Regularization
Citation
Fury, M. (2018). Logarithmic regularization of non-autonomous non-linear ill-posed problems in Hilbert spaces. <i>Electronic Journal of Differential Equations, 2018</i>(28), pp. 1-11.