TY - JOUR
T1 - A New Regularization Method for a Parameter Identification Problem in a Non-Linear Partial Differential Equation
AU - Nair , M. Thamban
AU - Roy , Samprita Das
JO - Journal of Partial Differential Equations
VL - 2
SP - 147
EP - 190
PY - 2023
DA - 2023/07
SN - 36
DO - http://doi.org/ 10.4208/jpde.v36.n2.3
UR - https://global-sci.org/intro/article_detail/jpde/21839.html
KW - Ill-posed, regularization, parameter identification.
AB - <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>