A new regularization method for a parameter identification problem in a
non-linear partial differential equation

- M Thamban Nair,
- Samprita Roy

## Abstract

We consider a parameter identification problem associated with a quasi-linear elliptic Neumann boundary value problem involving a parameter function \(a(\cdot)\) and the solution \(u(\cdot)\), where the problem is to identify \(a(\cdot)\) on an interval \(I:=g(\Gamma)\) from the knowledge of the solution \(u(\cdot)\) as \(g\) on \(\Gamma\), where \(\Gamma\) is a given curve on the boundary of the domain \(\Omega\subseteq{\mathbb{R}}^{3}\) of the problem and \(g\) is a continuous function. The inverse problem is formulated as a problem of solving an operator equation involving a compact operator depending on the data, and for obtaining stable approximate solutions under noisy data, a new regularization method is considered. The derived error estimates are similar to, and in certain cases better than, the classical Tikhonov regularization considered in the literature in the recent past.

01 Jun 2020Submitted to *Mathematical Methods in the Applied Sciences* 05 Jun 2020Assigned to Editor

05 Jun 2020Submission Checks Completed

11 Jun 2020Reviewer(s) Assigned