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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/2503.19849 |
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| _version_ | 1866918241421492224 |
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| author | Sulak, Anthony Turanova, Olga |
| author_facet | Sulak, Anthony Turanova, Olga |
| contents | We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an $L^4$ bound on the gradient of the pressure and an estimate of Aronson-Bénilan type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The incompressible limit of an inhomogeneous model of tissue growth Sulak, Anthony Turanova, Olga Analysis of PDEs We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an $L^4$ bound on the gradient of the pressure and an estimate of Aronson-Bénilan type. |
| title | The incompressible limit of an inhomogeneous model of tissue growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.19849 |