A variational method for identifying a spacewise-dependent heat source. (English) Zbl 1135.65034

Johansson, B. Tomas; Lesnic, Daniel

IMA J. Appl. Math. 72, No. 6, 748-760 (2007).

The authors consider the problem of identifying the spacewise-dependent right-hand side in a parabolic problem from the initial and final temperature distributions. This problem is ill-posed. The authors formulate the problem in a variational form and use the conjugate gradient method with an appropriate stopping rule in combination with boundary element methods to numerically solve the problem. Numerical results show that the method is efficient.

Reviewer: Dinh Nho Hao (Hanoi)

MSC:

65M32	Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05	Heat equation

Keywords:

boundary element method; conjugate gradient method; discrepancy principle; heat source; inverse problem; iterative regularization; parabolic heat equation; ill-posed problem; numerical results