Regularization methods for a class of ill-posed inverse problems
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Date
2024
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Publisher
Faculty of Sciences
Abstract
In the present memory, we investigate two classes of inverse problems. In the Örst class, we
study the inverse problem of identifying the unknown source in the Poisson equation. The
second class is devoted to the study of inverse problem for identifying the initial value on
the heat equation on the columnar symmetric domain. These problems are ill posed problem
in the sense of Hadamard. By using the quasi-boundary value method, we show that the
solutions of approximate problems have a stable character as well as their convergences
towards to the solutions of the original problems. Moreover, some convergence results are
established for the proposed methods.