@Article{JPDE-36-2,
author = {Thamban, Nair, M. and Samprita, Roy, Das},
title = {A New Regularization Method for a Parameter Identification Problem in a Non-Linear Partial Differential Equation},
journal = {Journal of Partial Differential Equations},
year = {2023},
volume = {36},
number = {2},
pages = {147--190},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-732X},
doi = {https://doi.org/ 10.4208/jpde.v36.n2.3},
url = {https://global-sci.com/article/88085/a-new-regularization-method-for-a-parameter-identification-problem-in-a-non-linear-partial-differential-equation}
}