On Regularization of a Source Identification Problem in a Parabolic PDE and Its Finite Dimensional Analysis
Year: 2021
Author: Subhankar Mondal, M. Thamban Nair
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 3 : pp. 240–257
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v34.n3.3
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 3 : pp. 240–257
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Ill-posed source identification Tikhonov regularization weak solution.