@article{Bazán2023, 
author = {Fermín S. V. Bazán and Luciano Bedin and Mansur I. Ismailov and Leonardo S. Borges},
title = {Inverse time-dependent source problem for the heat equation with a nonlocal Wentzell-Neumann boundary condition},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {4},
pages = {1747-1771},
keywords = {inverse heat transfer, Wentzell boundary conditions, Morozov's discrepancy principle, generalized cross validation, minimum product rule},
url = {https://www.sciopen.com/article/10.3934/nhm.2023076},
doi = {10.3934/nhm.2023076},
abstract = {In this work, we consider the problem of recovering the heat source term for the heat equation with a nonlocal Wentzell-Neumann boundary condition subject to an integral overdetermination condition. Conditions for the existence and uniqueness of the classical solution of the inverse problem are revisited, and a numerical method for practical source reconstruction is introduced. Unlike all of the source reconstruction methods found in literature, the method introduced in this work computes regularized solutions from a triangular linear system arising from a semi-discretization in the space of the continuous model. Regularization is introduced by applying the generalized singular value decomposition of a proper matrix pair along with truncation. Numerical results illustrate the effectiveness of the method.}
}