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


HASANOV A., Erdem A.

IMA JOURNAL OF APPLIED MATHEMATICS, cilt.73, ss.579-591, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 73 Konu: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1093/imamat/hxm056
  • Dergi Adı: IMA JOURNAL OF APPLIED MATHEMATICS
  • Sayfa Sayısı: ss.579-591

Özet

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.