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|data=$a Problema inverso da equação do calor com condição de contorno de Wentzell-Neumann $h [recurso eletrônico] / $c Mairon Carliel Pontarolo ; orientador, Luciano Bedin
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|data=$a Abstract: In this work, a study is conducted on the inverse problem of the heat equation with nonlocal Wentzell-Neumann boundary condition, from an integral overdetermination condition modeled as an energy function. The problem is approached from two aspects: theoretical/analytical and numerical/computational. In the first approach, sufficient conditions for the existence and uniqueness of the solution to both direct and inverse problems are established, resulting in two main theorems. In the second approach, a numerical model is introduced for the approximation of the source term, based on the semidiscretization of the continuous model and the midpoint method applied to the resulting initial value problem. To address the ill -conditioned problem and noisy data, the regularization method employed relies on the generalized singular value decomposition of a proper matrix pair. Regularization is performed through truncation, with the truncation parameter determined by the discrepancy principle. Finally, numerical examples are presented to illustrate the efficiency of the introduced numerical method.
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|authorityData150=$a Condição de contorno Wentzell-Neumann
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