Identification of the right-hand side in a bi-parabolic equation with final data. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Quoc Nam, Danh Hua; Dinh Long, Le; O'Regan, Donal; Bao Ngoc, Tran; Huy Tuan, Nguyen
• Is Part Of: Applicable analysis. Volume 101:Issue 4(2022)
• Page Start: 1157
• Page End: 1175
• Publication Date: 2022-03-04
• Subjects: Ill-posed problem -- bi-parabolic equation -- Tikhonov regularization; 35R30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1775817
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider the problem of finding the source distribution for the linear inhomogeneous biparabolic equation when the measured output data is given in the form of the final overdetermination. The problem is severely ill-posed in the sense of Hadamard. First, we apply a general filter method to regularize the linear nonhomogeneous problem. Then, we give a regularized solution and consider the convergence between the regularized solution and the sought solution. Under an a priori assumption on the exact solution, we obtain some convergence estimates between the regularized solution and the sought solution.