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.