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Inverse coefficient problems for elliptic variational inequalities with a nonlinear monotone operator. (English) Zbl 0912.35157

Summary: The class of inverse problems for a nonlinear elliptic variational inequality is considered. The nonlinear elliptic operator is assumed to be a monotone potential operator. 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 elastoplastic body is considered. For this problem the numerical method and computational results are also presented.

MSC:

35R30 Inverse problems for PDEs
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
74S30 Other numerical methods in solid mechanics (MSC2010)
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