On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis

• 作者: MONDAL Subhankar NAIR M.Thamban
• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 年，卷（期）: 2021,（3）
• 页码范围: 240-257
• 页数: 18页
• 分类号: O175.26
• 语种: 英文
• DOI: 10.4208/jpde.v34.n3.3

摘要

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 lin-ear 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 L2 (0,τ;L2(Ω)).For illus-trating 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.