Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

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HASANOV A., Erdem A.

IMA JOURNAL OF APPLIED MATHEMATICS, vol.73, no.4, pp.579-591, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1093/imamat/hxm056
  • Journal Name: IMA JOURNAL OF APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.579-591
  • Kocaeli University Affiliated: Yes

Abstract

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g(xi(2)) depends on the gradient xi: = vertical bar del u vertical bar of the solution u(x), x is an element of Omega subset of R(n), of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H(1)(Omega) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g(xi(2)) is obtained in the following sense: parallel to u(x;g) - u(x;g(m))parallel to(1) -> 0 when g(m)(eta) -> g(eta) point-wise as m -> infinity. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.