In this study, we consider an inverse problem of determining an unknown source function in the right-hand side of an elliptic equation which is ill-posed in the Hadamard sense. To investigate the solvability of the problem, we reduce it to a Dirichlet problem for a third-order partial differential equation with homogeneous boundary condition. Since the problem is linear, the proof of the uniqueness theorem is based on the Fredholm Alternative Theorem. We prove the existence of the solution to the problem by using the Galerkin method.
Primary Language | English |
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Subjects | Applied Mathematics (Other) |
Journal Section | Natural Sciences |
Authors | |
Publication Date | March 28, 2024 |
Submission Date | September 13, 2023 |
Acceptance Date | February 26, 2024 |
Published in Issue | Year 2024 |