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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.18870 |
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| _version_ | 1866913754829029376 |
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| author | David, Noemi Jacobs, Matt Kim, Inwon |
| author_facet | David, Noemi Jacobs, Matt Kim, Inwon |
| contents | In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our analysis is a family of energy evolution equations and their dissipation structures, which are novel and of independent interest. This strategy allows us to consider a larger family of pressure laws as well as proving the joint limit, from a compressible Brinkman's model to the incompressible Darcy's law, where the latter is a Hele-Shaw type free boundary problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the singular limit of Brinkman's law to Darcy's law David, Noemi Jacobs, Matt Kim, Inwon Analysis of PDEs In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our analysis is a family of energy evolution equations and their dissipation structures, which are novel and of independent interest. This strategy allows us to consider a larger family of pressure laws as well as proving the joint limit, from a compressible Brinkman's model to the incompressible Darcy's law, where the latter is a Hele-Shaw type free boundary problem. |
| title | On the singular limit of Brinkman's law to Darcy's law |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.18870 |