On a Differential Model for Sandpiles Growing in a Silo
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917275134590976 |
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| author | Crasta, Graziano Malusa, Annalisa |
| author_facet | Crasta, Graziano Malusa, Annalisa |
| contents | We discuss some features of a boundary value problem for a system of PDEs that describes the growth of a sandpile in a container under the action of a vertical source. In particular, we characterize the long-term behavior of the profiles, and we provide a sufficient condition on the vertical source that guarantees the convergence to the equilibrium in a finite time. We show by counterexamples that a stable configuration may not be reached in a finite time, in general, even if the source is time-independent. Finally, we provide a complete characterization of the equilibrium profiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Differential Model for Sandpiles Growing in a Silo Crasta, Graziano Malusa, Annalisa Analysis of PDEs 35C15, 35F30 We discuss some features of a boundary value problem for a system of PDEs that describes the growth of a sandpile in a container under the action of a vertical source. In particular, we characterize the long-term behavior of the profiles, and we provide a sufficient condition on the vertical source that guarantees the convergence to the equilibrium in a finite time. We show by counterexamples that a stable configuration may not be reached in a finite time, in general, even if the source is time-independent. Finally, we provide a complete characterization of the equilibrium profiles. |
| title | On a Differential Model for Sandpiles Growing in a Silo |
| topic | Analysis of PDEs 35C15, 35F30 |
| url | https://arxiv.org/abs/2509.24618 |