Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation
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| Format: | Preprint |
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2024
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| _version_ | 1866916110322892800 |
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| author | Zheng, Xiangcheng Li, Yiqun Qiu, Wenlin |
| author_facet | Zheng, Xiangcheng Li, Yiqun Qiu, Wenlin |
| contents | We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model resolves the incompatibility between the nonlocal operators in subdiffusion and the local initial conditions and thus eliminates the initial singularity of the solutions of the subdiffusion, while retaining its heavy tail behavior away from the initial time. The well-posedness of the model and high-order regularity estimates of its solutions are analyzed by resolvent estimates, based on which the numerical discretization and analysis are performed. Numerical experiments are carried out to substantiate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation Zheng, Xiangcheng Li, Yiqun Qiu, Wenlin Numerical Analysis 35R11, 65M12 We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model resolves the incompatibility between the nonlocal operators in subdiffusion and the local initial conditions and thus eliminates the initial singularity of the solutions of the subdiffusion, while retaining its heavy tail behavior away from the initial time. The well-posedness of the model and high-order regularity estimates of its solutions are analyzed by resolvent estimates, based on which the numerical discretization and analysis are performed. Numerical experiments are carried out to substantiate the theoretical findings. |
| title | Local modification of subdiffusion by initial Fickian diffusion: Multiscale modeling, analysis and computation |
| topic | Numerical Analysis 35R11, 65M12 |
| url | https://arxiv.org/abs/2401.16885 |