International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 25-32
doi:10.1155/S0161171295000020
A stability result for parameter identification problems in nonlinear parabolic problems
Institute for Information Siences, Jagellonian University, ul. Naswojki 11, Cracow 30072, Poland
Received 15 March 1993
Copyright © 1995 Stanislaw Migórski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A sequence of identification problems of coefficients in the parabolic equation with
nonlinear 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 solutions
exist and that under some continuous convergence of the cost functionals and the convergence of
the data, the sets of optimal solutions converge in some sense to the set of optimal solutions of
the limit problem.