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A sequence of identification problems of coefficients in the parabolic equation withnonlinear boundary conditions is considered. The parameter (index of an element of the sequence)appears in the cost functionals as well as boundary data. It is proved that the optimal solutionsexist and that under some continuous convergence of the cost functionals and the convergence ofthe data, the sets of optimal solutions converge in some sense to the set of  optimal solutions ofthe limit problem

A stability result for parameter identification problems in nonlinear parabolic problems