Modified Quasi Boundary Value method for inverse source biparabolic
In this study, we study an inverse source problem of the bi-parabolic equation. The problem is severely non-well-posed in the sense of Hadamard, the problem is called well-posed if it satisfies three conditions, such as the existence, the uniqueness, and the stability of the solution. If one of th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
ATNAA
2020-07-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1212311 |
| Summary: | In this study, we study an inverse source problem of the bi-parabolic equation. The problem is severely
non-well-posed in the sense of Hadamard, the problem is called well-posed if it satisfies three conditions,
such as the existence, the uniqueness, and the stability of the solution. If one of the these properties is
not satisfied, the problem is called is non well-posed (ill-posed). According to our research experience, the
stability properties of the sought solution are most often violated. Therefore, a regularization method is
required. Here, we apply a Modified Quasi Boundary Method to deal with the inverse source problem.
Base on this method, we give a regularized solution and we show that the regularized solution satisfies the
conditions of the well-posed problem in the sense of Hadarmad. In addition, we present the estimation
between the regularized solution and the sought solution by using a priori regularization parameter choice
rule.
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| ISSN: | 2587-2648 2587-2648 |