A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910461005398016 |
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| author | Alavani, Vighnesh V. Danumjaya, P. Nair, M. Thamban |
| author_facet | Alavani, Vighnesh V. Danumjaya, P. Nair, M. Thamban |
| contents | Recently, Nair and Danumjaya (2023) introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable, for determining the initial value function. In this paper, the authors extend the analysis done in the above referred paper to a more general setting of an inhomogeneous time-fractional heat equation involving the higher dimensional state variables and a general elliptic operator. We carry out the analysis for the newly introduced regularization method for the TFBHCP providing optimal order error estimates under a source condition by choosing the regularization parameter appropriately, and also carry out numerical experiments illustrating the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function Alavani, Vighnesh V. Danumjaya, P. Nair, M. Thamban Analysis of PDEs Numerical Analysis 35K57, 35R25, 35R30, 65J20 Recently, Nair and Danumjaya (2023) introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable, for determining the initial value function. In this paper, the authors extend the analysis done in the above referred paper to a more general setting of an inhomogeneous time-fractional heat equation involving the higher dimensional state variables and a general elliptic operator. We carry out the analysis for the newly introduced regularization method for the TFBHCP providing optimal order error estimates under a source condition by choosing the regularization parameter appropriately, and also carry out numerical experiments illustrating the theoretical results. |
| title | A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function |
| topic | Analysis of PDEs Numerical Analysis 35K57, 35R25, 35R30, 65J20 |
| url | https://arxiv.org/abs/2405.18074 |