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, cilt.29, sa.1, ss.81-91, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1515/jiip-2020-0047
  • Dergi Adı: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.81-91
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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