Inverse coefficient problems for elliptic variational inequalities with a nonlinear monotone operator

Hasanov A.

INVERSE PROBLEMS, vol.14, no.5, pp.1151-1169, 1998 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 5
  • Publication Date: 1998
  • Doi Number: 10.1088/0266-5611/14/5/005
  • Journal Name: INVERSE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1151-1169
  • Kocaeli University Affiliated: No

Abstract

The class of inverse problems for a nonlinear elliptic variational inequality is considered. The nonlinear elliptic operator is assumed to be a monotone potential. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients which is compact in H-1(0, xi*). It is shown that the nonlinear operator is pseudomonotone for the given class of coefficients. For the corresponding direct problem H-1- coefficient convergence is proved. Based on this result the existence of a quasisolution of the inverse problem is obtained. As an important application an inverse diagnostic problem for an axially symmetric elasto-plastic body is considered. For this problem the numerical method and computational results are also presented.