“A heat source reconstruction formula from single internal measurements using a family of null controls”

Research areas:
Year:
2013
Type of Publication:
Article
Authors:
  • García G. C.
  • Osses A.
  • Tapia M.
Journal:
Journal of Inverse and Ill-posed Problems
Volume:
21
Pages:
755–779
Month:
January
ISSN:
0928-0219
Abstract:
We consider the inverse problem of determining the spatial dependence f of the source term in a heat equation known, from a single internal measurements of the solution. The purpose of this paper is to establish a reconstruction formula for f similar to the one obtained by M. Yamamoto in “Stability, Reconstruction formula and regularization for an inverse source hyperbolic problem by a control method”, Inverse Problems 11 (1995), 481–496, for hyperbolic equations using exact controls, and generalized here for parabolic equations. The reconstruction formula is associated to a family of exact controls v indexed by \tau. We perform numerical simulations in order to illustrate the feasibility, accuracy and stability of the proposed reconstruction formula.