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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.