Mathematical model for collective migration on a viscoelastic collagen network
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929686182887424 |
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| author | Meunier, Nicolas Tarfulea, Andrei |
| author_facet | Meunier, Nicolas Tarfulea, Andrei |
| contents | In this paper, we study a model of self-generated directional cell migration on viscoelastic substrates in the absence of apparent intrinsic polarity. This model, first proposed in \cite{Clark}, was observed numerically to manifest traveling pulse solutions for sufficiently large collagen stiffness, leading to a persistent collective migration. Here we provide a rigorous mathematical framework for the model, finding the exact stationary states and conditional traveling pulse. We also prove global well-posed in $W^{k,\infty}$ spaces, local stability of the traveling pulse for high stiffness, and exponential convergence to the stationary state for low stiffness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical model for collective migration on a viscoelastic collagen network Meunier, Nicolas Tarfulea, Andrei Analysis of PDEs In this paper, we study a model of self-generated directional cell migration on viscoelastic substrates in the absence of apparent intrinsic polarity. This model, first proposed in \cite{Clark}, was observed numerically to manifest traveling pulse solutions for sufficiently large collagen stiffness, leading to a persistent collective migration. Here we provide a rigorous mathematical framework for the model, finding the exact stationary states and conditional traveling pulse. We also prove global well-posed in $W^{k,\infty}$ spaces, local stability of the traveling pulse for high stiffness, and exponential convergence to the stationary state for low stiffness. |
| title | Mathematical model for collective migration on a viscoelastic collagen network |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.13892 |