Identification of the right-hand side in a bi-parabolic equation with final data

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.

Keywords:

• Ill-posed problem
• bi-parabolic equation
• Tikhonov regularization

2010 Mathematics Subject Classification:

• 35R30

Disclosure statement

No potential conflict of interest was reported by the author(s).