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Keywords:
inverse source problem; nonlinear parabolic equation; memory term; optimal control
inverse source problem; nonlinear parabolic equation; memory term; optimal control
Summary:
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 of this approach.
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