Regularization Method for Identifying the Source Term in Parabolic Equations during Heat Conduction Processes
The heat source in the parabolic heat equation during the heat conduction process is reconstructed using the final measured temperature,and the inverse problem is transformed into an optimization problem using the total variation regularization method.The necessary condition for the existence of the minimum value of the objective functional is derived by introducing a polished total variation regularization term.The necessary conditions for the existence of the minimum value are used to prove the uniqueness and stability of the minimal element.
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