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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.16416 |
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| _version_ | 1866912595445809152 |
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| author | Lai, Chen-Chih Lu, Hongbo |
| author_facet | Lai, Chen-Chih Lu, Hongbo |
| contents | We rigorously derive the joint limit of vanishing viscosity, singular pressure, and discrete-to-continuous phenotype structure in a class of tissue growth models. Starting from a viscoelastic (Brinkman-type) system describing multiple interacting phenotypes, where pressure depends nonlinearly on total cell density, we establish convergence to an incompressible Darcy-type model with a continuous phenotypic structure. Our analysis builds upon recent advances on the Brinkman-to-Darcy limit and incompressible transitions by David, Jacob, and Kim [arXiv:2503.18870], and on hydrodynamic limits for phenotype-structured populations by Debiec, Mandal, and Schmidtchen [J. Differential Equations 2025]. A key novelty lies in combining all three singular limits simultaneously, under uniform a priori estimates, compactness in space-phenotype-time, and a generalized entropy-dissipation structure. This provides a unified framework for modeling constrained tissue growth with mechanical feedback and phenotypic plasticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint inviscid, incompressible, and continuous phenotype limit in nonlocal models of tissue growth Lai, Chen-Chih Lu, Hongbo Analysis of PDEs We rigorously derive the joint limit of vanishing viscosity, singular pressure, and discrete-to-continuous phenotype structure in a class of tissue growth models. Starting from a viscoelastic (Brinkman-type) system describing multiple interacting phenotypes, where pressure depends nonlinearly on total cell density, we establish convergence to an incompressible Darcy-type model with a continuous phenotypic structure. Our analysis builds upon recent advances on the Brinkman-to-Darcy limit and incompressible transitions by David, Jacob, and Kim [arXiv:2503.18870], and on hydrodynamic limits for phenotype-structured populations by Debiec, Mandal, and Schmidtchen [J. Differential Equations 2025]. A key novelty lies in combining all three singular limits simultaneously, under uniform a priori estimates, compactness in space-phenotype-time, and a generalized entropy-dissipation structure. This provides a unified framework for modeling constrained tissue growth with mechanical feedback and phenotypic plasticity. |
| title | Joint inviscid, incompressible, and continuous phenotype limit in nonlocal models of tissue growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.16416 |