Relation between generalized diffusion equations and subordination schemes
- Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology, and earth sciences. Some of such processes (notably, the fluid limits of continuous time random walks) allow for either kind of description, but other ones do not. In the present work we discuss the conditions under which a generalized diffusion equation does correspond to a subordination scheme, and the conditions under which a subordination scheme does possess the corresponding generalized diffusion equation. Moreover, we discuss examples of random processes for which only one, or both kinds of description are applicable.
| Author details: | Aleksei V. ChechkinORCiDGND, Igor M. SokolovORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1103/PhysRevE.103.032133 |
| ISSN: | 2470-0045 |
| ISSN: | 2470-0053 |
| Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
| Publisher: | American Physical Society |
| Place of publishing: | College Park |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/03/19 |
| Publication year: | 2021 |
| Release date: | 2023/11/10 |
| Volume: | 103 |
| Issue: | 3 |
| Article number: | 032133 |
| Number of pages: | 10 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| 5 Naturwissenschaften und Mathematik / 57 Biowissenschaften; Biologie / 570 Biowissenschaften; Biologie | |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
