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, vol.26, pp.349-368, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1515/jiip-2017-0106
  • Title of Journal : JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
  • Page Numbers: pp.349-368

Abstract

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