Logarithmic convexity of non-symmetric time-fractional diffusion equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916217316442112 |
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| author | Chorfi, S. E. Maniar, L. Yamamoto, M. |
| author_facet | Chorfi, S. E. Maniar, L. Yamamoto, M. |
| contents | We consider a class of diffusion equations with the Caputo time-fractional derivative $\partial_t^αu=L u$ subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order $0<α< 1$ and a second-order operator $L$ which is elliptic and non-symmetric. In this paper, we show that the logarithmic convexity extends to this non-symmetric case provided that the drift coefficient is given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non-symmetric cases. Finally, some conclusions and open problems will be mentioned. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic convexity of non-symmetric time-fractional diffusion equations Chorfi, S. E. Maniar, L. Yamamoto, M. Analysis of PDEs 35R11, 35R30, 35R25 We consider a class of diffusion equations with the Caputo time-fractional derivative $\partial_t^αu=L u$ subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order $0<α< 1$ and a second-order operator $L$ which is elliptic and non-symmetric. In this paper, we show that the logarithmic convexity extends to this non-symmetric case provided that the drift coefficient is given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non-symmetric cases. Finally, some conclusions and open problems will be mentioned. |
| title | Logarithmic convexity of non-symmetric time-fractional diffusion equations |
| topic | Analysis of PDEs 35R11, 35R30, 35R25 |
| url | https://arxiv.org/abs/2404.14046 |