Simultaneously identifying the thermal conductivity and radiative coefficient in heat equation from Dirichlet and Neumann boundary measured outputs


Hasanov A.

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, vol.29, no.1, pp.81-91, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1515/jiip-2020-0047
  • Title of Journal : JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
  • Page Numbers: pp.81-91

Abstract

This paper deals with an inverse coefficient problem of simultaneously identifying the thermal conductivity k(x) and radiative coefficient q(x) in the 1D heat equation u(t) = (k(x)u(x))(x) - q(x)u from the most available Dirichlet and Neumann boundary measured outputs. The Neumann-to-Dirichlet and Neumann-to-Neumann operators Phi[k, q](t) := u(l, t; k, q), Psi[k, q](t) := -k(0)u(x)(0, t; k, q) are introduced, and main properties of these operators are derived. Then the Tikhonov functional