Lipschitz continuity of the Frechet gradient in an inverse coefficient problem for a parabolic equation with Dirichlet measured output


Hasanov A.

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, cilt.26, ss.349-368, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 26 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1515/jiip-2017-0106
  • Dergi Adı: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
  • Sayfa Sayıları: ss.349-368

Özet

This paper studies the Lipschitz continuity of the Frechet gradient of the Tikhonov functional J(k) := (1/2)parallel to u(0, .; k) - f parallel to(2)(L2)((0, T)) corresponding to an inverse coefficient problem for the 1D parabolic equation u(t) = (k(x)u(x))(x) with the Neumann boundary conditions - k(0) u(x)(0, t) = g(t) and u(x)(l, t) = 0. In addition, compactness and Lipschitz continuity of the input-output operator