On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis |
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| Authors: | Subhankar Mondal & M. Thamban Nair |
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| Affiliation: | Department of Mathematics,IIT Madras,Chennai 600036,India |
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| 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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| Keywords: | Ill-posed source identification Tikhonov regularization weak solution. |
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