On nonlinear Sobolev equations with terminal observations in \(L^p\) spaces
- Authors
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- Keywords:
- Conformable derivative, Fourier truncation method, Regularization
- Abstract
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In this paper, we investigate the backward problem for the heat equation equipped with the time fractional conformable derivative. This problem is a generalization of the classical heat equation. We consider the problem with a nonlinear source function in a bounded domain. This problem is shown to be ill-posed, so we regularize the solution by the Fourier truncated method and we estimate the error term in the \(L^p(\mathcal{D})\) space. An example to illustrate the theory is given in the final section.
- References
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- Additional Files
- Published
- 28-03-2025
- Issue
- Vol. 1 No. 1 (2023)
- Section
- Research Article
- License
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Copyright (c) 2023 Letters on Applied and Pure Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.
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