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In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness...
We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
We consider the identification of a distributed parameter in an elliptic
variational inequality. On the basis of an optimal control problem
formulation, the application of a primal-dual penalization
technique enables us to prove the existence
of multipliers giving a first order characterization of the optimal solution.
Concerning the parameter we consider different
regularity requirements. For the numerical realization we utilize a complementarity function,
which allows us to rewrite the optimality...
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