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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06030 |
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| _version_ | 1866915606524067840 |
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| author | Łupińska, Barbara Rybka, Piotr |
| author_facet | Łupińska, Barbara Rybka, Piotr |
| contents | We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line. Depending on the boundary condition, we show that solutions converge in $L^p$, $p>1$ to a multiple of the self-similar solutions or decay to zero. The convergence rate is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of solutions to a space fractional diffusion equation Łupińska, Barbara Rybka, Piotr Analysis of PDEs 35R11 35A0 We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line. Depending on the boundary condition, we show that solutions converge in $L^p$, $p>1$ to a multiple of the self-similar solutions or decay to zero. The convergence rate is provided. |
| title | Asymptotic behavior of solutions to a space fractional diffusion equation |
| topic | Analysis of PDEs 35R11 35A0 |
| url | https://arxiv.org/abs/2511.06030 |