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A New Regularization Method for a Parameter Identification Problem in a Non-Linear Partial Differential Equation

A New Regularization Method for a Parameter Identification Problem in a Non-Linear Partial Differential Equation

Year:    2023

Author:    M. Thamban Nair, Samprita Das Roy

Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 147–190

Abstract

We consider a parameter identification problem associated with a quasilinear elliptic Neumann boundary value problem involving a parameter function $a(·)$ and the solution $u(·),$ where the problem is to identify $a(·)$ on an interval $I:=g(Γ)$ from the knowledge of the solution $u(·)$ as $g$ on $Γ,$ where Γ is a given curve on the boundary of the domain $Ω⊆\mathbb{R}^3$ 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 recent past.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/ 10.4208/jpde.v36.n2.3

Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 2 : pp. 147–190

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    44

Keywords:    Ill-posed regularization parameter identification.

Author Details

M. Thamban Nair

Samprita Das Roy