Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911083765170176 |
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| author | Blawid, Julian Dolzmann, Georg |
| author_facet | Blawid, Julian Dolzmann, Georg |
| contents | Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure growth is determined by means of a family of ordinary differential equations in every point in space. Subsequently, an elastic deformation, which is given by the minimizer of a hyperelastic variational integral, is applied in order to restore Dirichlet boundary conditions. While the ordinary differential equations governing the growth process depend on the elastic stress and the pullback of a nutrient concentration in the current configuration, the hyperelastic variational problem is solved on the intermediate configuration after pure growth. Additionally, the coefficients of the reaction-diffusion equation determining the nutrient concentration in the current configuration depend on the elastic deformation and the deformation due to pure growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension Blawid, Julian Dolzmann, Georg Analysis of PDEs Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure growth is determined by means of a family of ordinary differential equations in every point in space. Subsequently, an elastic deformation, which is given by the minimizer of a hyperelastic variational integral, is applied in order to restore Dirichlet boundary conditions. While the ordinary differential equations governing the growth process depend on the elastic stress and the pullback of a nutrient concentration in the current configuration, the hyperelastic variational problem is solved on the intermediate configuration after pure growth. Additionally, the coefficients of the reaction-diffusion equation determining the nutrient concentration in the current configuration depend on the elastic deformation and the deformation due to pure growth. |
| title | Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.22582 |