@Article{JPDE-34-3,
author = {Subhankar, Mondal and Thamban, Nair, M.},
title = {On Regularization of a Source Identification Problem in a Parabolic PDE and Its Finite Dimensional Analysis},
journal = {Journal of Partial Differential Equations},
year = {2021},
volume = {34},
number = {3},
pages = {240--257},
abstract = {<p style="text-align: justify;">We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v34.n3.3},
url = {https://global-sci.com/article/88140/on-regularization-of-a-source-identification-problem-in-a-parabolic-pde-and-its-finite-dimensional-analysis}
}