An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Zui-Cha Deng
  • Y. C. Hon
  • Liu Yang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)890-910
Journal / PublicationJournal of Optimization Theory and Applications
Volume160
Issue number3
Online published19 Apr 2013
Publication statusPublished - Mar 2014

Abstract

This paper investigates the solution of a parameter identification problem associated with the two-dimensional heat equation with variable diffusion coefficient. The singularity of the diffusion coefficient results in a nonlinear inverse problem which makes theoretical analysis rather difficult. Using an optimal control method, we formulate the problem as a minimization problem and prove the existence and uniqueness of the solution in weighted Sobolev spaces. The necessary conditions for the existence of the minimizer are also given. The results can be extended to more general parabolic equations with singular coefficients. © 2013 Springer Science+Business Media New York.

Research Area(s)

  • Existence, Nonlinear inverse coefficient problem, Optimal control, Singularity, Uniqueness

Citation Format(s)

An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem. / Deng, Zui-Cha; Hon, Y. C.; Yang, Liu.
In: Journal of Optimization Theory and Applications, Vol. 160, No. 3, 03.2014, p. 890-910.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review