Fractional diffusion equations interpolate between damping and waves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910644891025408 |
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| author | Manapany, Andy Fumeron, Sébastien Henkel, Malte |
| author_facet | Manapany, Andy Fumeron, Sébastien Henkel, Malte |
| contents | The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional diffusion equations interpolate between damping and waves Manapany, Andy Fumeron, Sébastien Henkel, Malte Mathematical Physics Statistical Mechanics High Energy Physics - Theory The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times. |
| title | Fractional diffusion equations interpolate between damping and waves |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.04887 |