TY - JOUR
T1 - On Regularization of a Source Identification Problem in a Parabolic PDE and Its Finite Dimensional Analysis
AU - Mondal , Subhankar
AU - Nair , M. Thamban
JO - Journal of Partial Differential Equations
VL - 3
SP - 240
EP - 257
PY - 2021
DA - 2021/07
SN - 34
DO - http://doi.org/10.4208/jpde.v34.n3.3
UR - https://global-sci.org/intro/article_detail/jpde/19322.html
KW - Ill-posed, source identification, Tikhonov regularization, weak solution.
AB - <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>