Deriving sub-diffusion equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909709074694144 |
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| author | Perthame, Benoît Tang, Min |
| author_facet | Perthame, Benoît Tang, Min |
| contents | Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is to provide the microscopic mechanism and rigorous derivation of sub-diffusions when the waiting time distribution of particles follows an age-structured equation and jumps occur at each renewal. The major difficulty to recover sub-diffusions, unlike normal diffusions, is that the assumption of long waiting time implies lack of integrability for the age equilibrium. This prevents to establish strong a priori estimates. Here, the Laplace transform plays the role that Fourier transform plays for the more traditional case of fast diffusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deriving sub-diffusion equations Perthame, Benoît Tang, Min Analysis of PDEs Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is to provide the microscopic mechanism and rigorous derivation of sub-diffusions when the waiting time distribution of particles follows an age-structured equation and jumps occur at each renewal. The major difficulty to recover sub-diffusions, unlike normal diffusions, is that the assumption of long waiting time implies lack of integrability for the age equilibrium. This prevents to establish strong a priori estimates. Here, the Laplace transform plays the role that Fourier transform plays for the more traditional case of fast diffusions. |
| title | Deriving sub-diffusion equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.20602 |