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

作　　者：MONDAL Subhankar NAIR M.Thamban 

机构地区：[1]Department of Mathematics,IIT Madras,Chennai 600036,India

出　　处：《Journal of Partial Differential Equations》2021年第3期240-257,共18页偏微分方程（英文版）

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 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,τ;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.

关 键 词：ILL-POSED source identification Tikhonov regularization weak solution 

分 类 号：O175.26[理学—数学]